Problem: Find all factor pairs of 64.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are the numbers you multiply together to get another number. We need to think about all the different whole numbers that divide evenly into 64.

* **1 and 64:**  1 x 64 = 64
* **2 and 32:** 2 x 32 = 64
* **4 and 16:** 4 x 16 = 64
* **8 and 8:** 8 x 8 = 64 

### Answer: (1, 64), (2, 32), (4, 16), (8, 8) 

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? Yes

Problem: List all the factor pairs of 18.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that, when multiplied together, equal the given number. Let's find all the factor pairs of 18:
* 1 x 18 = 18
* 2 x 9 = 18
* 3 x 6 = 18

### Answer: (1, 18), (2, 9), (3, 6)

Expected answer: [(1, 18), (2, 9), (3, 6)]

Correct? Yes

Problem: Find all factor pairs of 28.

Gemini-1.5 Pro:

Reasoning: Factor pairs are numbers that multiply together to get the original number. We need to find all pairs of numbers that have a product of 28. 
Let's start with 1:
* 1 x 28 = 28

Next is 2:
* 2 x 14 = 28

We can continue dividing 28 by larger numbers but we will be repeating the same pairs we already found. 

Therefore, the factor pairs of 28 are: 1 and 28, 2 and 14, 4 and 7.

### Answer: (1, 28), (2, 14), (4, 7) 

Expected answer: [(1, 28), (2, 14), (4, 7)]

Correct? Yes

Problem: List all factor pairs of the number 48.

Gemini-1.5 Pro:

A factor pair of 48 is any two whole numbers that multiply together to result in 48. Here's the complete list:

* 1 and 48 (1 x 48 = 48)
* 2 and 24 (2 x 24 = 48)
* 3 and 16 (3 x 16 = 48)
* 4 and 12 (4 x 12 = 48)
* 6 and 8  (6 x 8 = 48)

### Answer: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8) 

Expected answer: [(1, 48), (2, 24), (3, 16), (4, 12), (6, 8)]

Correct? Yes

Problem: Write down all factor pairs of 7.

Gemini-1.5 Pro:

Since 7 is a prime number, it only has two factors: 1 and itself. 

### Answer: (1, 7) 

Expected answer: [(1, 7)]

Correct? Yes

Problem: Write down every pair of factors of 98.

Gemini-1.5 Pro:

The factors of a number are the numbers that divide evenly into that number.  Here are the pairs of factors of 98:

* **1 and 98** (because 1 x 98 = 98)
* **2 and 49** (because 2 x 49 = 98)
* **7 and 14** (because 7 x 14 = 98) 

Expected answer: [(1, 98), (2, 49), (7, 14)]

Correct? No

Problem: List all the factor pairs of the number 26.

Gemini-1.5 Pro:

A factor pair of 26 is two whole numbers that when multiplied, will result in 26.

* 1 x 26 = 26
* 2 x 13 = 26

### Answer: (1, 26), (2, 13) 

Expected answer: [(1, 26), (2, 13)]

Correct? Yes

Problem: Write down all factor pairs of 59.

Gemini-1.5 Pro:

Reasoning:  A factor pair of 59 is any two whole numbers that multiply to give 59. Since 59 is a prime number, it only has two factors: 1 and itself. 
### Answer: (1, 59) 

Expected answer: [(1, 59)]

Correct? Yes

Problem: Find out all factor pairs of 20.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are the numbers that can be multiplied together to get 20. 
* 1 x 20 = 20
* 2 x 10 = 20
* 4 x 5 = 20

### Answer: (1, 20), (2, 10), (4, 5)

Expected answer: [(1, 20), (2, 10), (4, 5)]

Correct? Yes

Problem: Write down all factor pairs of 20.

Gemini-1.5 Pro:

A factor pair of 20 is any two whole numbers that multiply to give 20. Here is the complete list:

* 1 and 20
* 2 and 10
* 4 and 5 

Expected answer: [(1, 20), (2, 10), (4, 5)]

Correct? No

Problem: Please list down all factor pairs of 13.

Gemini-1.5 Pro:

Reasoning: The factors of a number divide evenly into that number.  Since 13 is a prime number, it only has two factors: 1 and itself.
### Answer: (1, 13) 

Expected answer: [(1, 13)]

Correct? Yes

Problem: Find all factor pairs of 81.

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of whole numbers that multiply to give 81.

* 1 and 81 (because 1 x 81 = 81)
* 3 and 27 (because 3 x 27 = 81)
* 9 and 9 (because 9 x 9 = 81)

### Answer: (1, 81), (3, 27), (9, 9) 

Expected answer: [(1, 81), (3, 27), (9, 9)]

Correct? Yes

Problem: List all factor pairs of 76.

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of whole numbers that multiply together to give 76.  Let's start with 1 and work our way up.

* 1 and 76:  1 * 76 = 76
* 2 and 38:  2 * 38 = 76
* 4 and 19:  4 * 19 = 76 

Since there are no other whole numbers between 4 and 19 that divide evenly into 76, we have found all the factor pairs. 

### Answer: (1, 76), (2, 38), (4, 19) 

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

Problem: Write down all factor pairs of 50.

Gemini-1.5 Pro:

A factor pair of 50 is any two numbers that when multiplied give us 50. Let's find all such pairs:

* 1 * 50 = 50
* 2 * 25 = 50
* 5 * 10 = 50

So, the factor pairs of 50 are:

### Answer: (1, 50), (2, 25), (5, 10) 

Expected answer: [(1, 50), (2, 25), (5, 10)]

Correct? Yes

Problem: List all the factor pairs of the number 76.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that you can multiply together to get the original number. Let's find all the pairs for 76:
* 1 and 76 (1 x 76 = 76)
* 2 and 38 (2 x 38 = 76)
* 4 and 19 (4 x 19 = 76)
### Answer: (1, 76), (2, 38), (4, 19) 

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

Problem: List all factor pairs of 56.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are numbers that multiply together to produce a target number (in this case, 56).  Let's find all the factor pairs of 56:
 
 * 1 and 56 (because 1 x 56 = 56)
 * 2 and 28 (because 2 x 28 = 56)
 * 4 and 14 (because 4 x 14 = 56)
 * 7 and 8 (because 7 x 8 = 56)
 
 ### Answer: (1, 56), (2, 28), (4, 14), (7, 8) 

Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]

Correct? Yes

Problem: List all the factor pairs of the number 44.

Gemini-1.5 Pro:

A factor pair of 44 is two whole numbers that when multiplied, equal 44. They are:

* 1 and 44 (1 x 44 = 44)
* 2 and 22 (2 x 22 = 44)
* 4 and 11 (4 x 11 = 44)

### Answer: (1, 44), (2, 22), (4, 11) 

Expected answer: [(1, 44), (2, 22), (4, 11)]

Correct? Yes

Problem: List all the factor pairs of 5.

Gemini-1.5 Pro:

The factors of a number divide evenly into that number. 

* 1 divides evenly into 5.
* 5 divides evenly into 5.

### Answer: (1, 5)

Expected answer: [(1, 5)]

Correct? Yes

Problem: Identify all factor pairs of the number 95.

Gemini-1.5 Pro:

Reasoning: A factor pair of 95 is any two whole numbers that, when multiplied together, have a product of 95. Since 95 is a product of two prime numbers (5 and 19), it only has two factor pairs. 

Here is the list of all factor pairs:
1 and 95, 
5 and 19

### Answer: (1,95), (5,19)

Expected answer: [(1, 95), (5, 19)]

Correct? No

Problem: Please list all the factor pairs of 36.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are the pairs of numbers that, when multiplied together, result in the original number. We can find them systematically by starting with 1 and its pair (36/1 = 36), then proceeding to 2 and its pair (36/2 = 18), and so on.

Here is the list of factor pairs of 36:
1 x 36
2 x 18
3 x 12
4 x 9
6 x 6

### Answer: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) 

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

Problem: Compute all the factor pairs of the number 59.

Gemini-1.5 Pro:

Reasoning:  A factor pair is a set of two numbers that, when multiplied together, equal the original number. 59 is a prime number, which means its only factors are 1 and itself. 
### Answer: (1, 59) 

Expected answer: [(1, 59)]

Correct? Yes

Problem: What are all the factor pairs of 3?

Gemini-1.5 Pro:

Reasoning: The factors of a number divide evenly into that number.  The only numbers that divide evenly into 3 are 1 and 3. 

### Answer: (1, 3) 

Expected answer: [(1, 3)]

Correct? Yes

Problem: Could you list all factor pairs of 51?

Gemini-1.5 Pro:

Reasoning: Factor pairs of 51 are the two whole numbers that multiply together to get 51.  Let's find all the factors of 51 first and then list them in pairs.
* 1 and 51 are factors of 51 because 1 x 51 = 51. 
* 3 and 17 are factors of 51 because 3 x 17 = 51.

### Answer: (1, 51), (3, 17) 

Expected answer: [(1, 51), (3, 17)]

Correct? Yes

Problem: List all factor pairs of 50.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are numbers that, when multiplied, equal the original number. Let's find all the factor pairs of 50.

* 1 x 50 = 50
* 2 x 25 = 50
* 5 x 10 = 50

### Answer: (1, 50), (2, 25), (5, 10) 

Expected answer: [(1, 50), (2, 25), (5, 10)]

Correct? Yes

Problem: Write down all factor pairs of 47.

Gemini-1.5 Pro:

Reasoning: The only factor pair of 47 is 1 and 47 because it is a prime number. 
### Answer: (1, 47)

Expected answer: [(1, 47)]

Correct? Yes

Problem: Write down all factor pairs of 51.

Gemini-1.5 Pro:

Reasoning: The factor pairs of a whole number are two numbers which multiply together to result in that number. 
The factor pairs of 51 are:
1 and 51 (because 1 x 51 = 51)
3 and 17 (because 3 x 17 = 51)
### Answer: (1, 51), (3, 17) 

Expected answer: [(1, 51), (3, 17)]

Correct? Yes

Problem: List all factor pairs of 60.

Gemini-1.5 Pro:

Here are the factor pairs of 60:

* **1 and 60** (1 * 60 = 60)
* **2 and 30** (2 * 30 = 60)
* **3 and 20** (3 * 20 = 60)
* **4 and 15** (4 * 15 = 60)
* **5 and 12** (5 * 12 = 60)
* **6 and 10** (6 * 10 = 60) 

### Answer: (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) 

Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]

Correct? Yes

Problem: List all factor pairs of 43.

Gemini-1.5 Pro:

Reasoning: The factors of a number are the numbers that divide evenly into that number. 
We need to check for all the numbers that divide 43 evenly. 
43 is a prime number, meaning its only factors are 1 and itself. 

### Answer: (1, 43)

Expected answer: [(1, 43)]

Correct? Yes

Problem: List all factor pairs of 70.

Gemini-1.5 Pro:

A factor pair of 70 is any two whole numbers that multiply together to equal 70.  Let's list them out systematically:

* **1 and 70:** 1 * 70 = 70
* **2 and 35:** 2 * 35 = 70
* **5 and 14:** 5 * 14 = 70
* **7 and 10:** 7 * 10 = 70

### Answer: (1, 70), (2, 35), (5, 14), (7, 10) 

Expected answer: [(1, 70), (2, 35), (5, 14), (7, 10)]

Correct? Yes

Problem: Please list all the factors of the number 2.

Gemini-1.5 Pro:

The factors of a number are all the numbers that divide evenly into that number.  

The number 2 is prime, meaning its only factors are 1 and itself.

### Answer: 1, 2 

Expected answer: [(1, 2)]

Correct? Yes

Problem: List all the factor pairs of 49.

Gemini-1.5 Pro:

The factors of a number are any numbers that divide into it exactly.
 
 49 is only divisible by 1, 7, and 49.  Therefore the factor pairs are:
 
 1 and 49 (1 x 49 = 49)
 7 and 7 (7 x 7 = 49)
 
 ### Answer: (1, 49), (7, 7) 
 

Expected answer: [(1, 49), (7, 7)]

Correct? Yes

Problem: Identify all factor pairs of 17.

Gemini-1.5 Pro:

Reasoning: A factor pair of 17 is any two whole numbers that multiply together to equal 17.  The only factor pair of 17 is 1 and 17.
### Answer: 1 and 17 

Expected answer: [(1, 17)]

Correct? Yes

Problem: Find all the factor pairs of 35.

Gemini-1.5 Pro:

Reasoning: Factor pairs are the numbers you multiply to get another number.  Let's find all the pairs for 35.
 
 * 1 x 35 = 35
 * 5 x 7 = 35
 
 ### Answer: (1, 35), (5, 7) 

Expected answer: [(1, 35), (5, 7)]

Correct? Yes

Problem: Identify all factor pairs of the number 91.

Gemini-1.5 Pro:

Reasoning: 
* A factor pair is a set of two numbers that, when multiplied, result in the original number.
* We need to find all the numbers that divide evenly into 91.
* 1 and 91 are obvious factors.
* Checking other numbers, we find that 7 and 13 also divide evenly into 91.

Therefore, the factor pairs of 91 are:
* 1 and 91
* 7 and 13 

### Answer: (1, 91), (7, 13) 

Expected answer: [(1, 91), (7, 13)]

Correct? Yes

Problem: List all factor pairs of the number 97.

Gemini-1.5 Pro:

Reasoning: The factors of a number are the numbers that divide evenly into that number. Since 97 is a prime number, it only has two factors: 1 and itself. 

### Answer: (1, 97) 

Expected answer: [(1, 97)]

Correct? Yes

Problem: What are all the factor pairs of 16?

Gemini-1.5 Pro:

Reasoning: Factor pairs are the numbers you can multiply together to get another number. To find all the factor pairs of 16, we need to think of all the different whole number multiplications that result in 16.
* 1 * 16 = 16 
* 2 * 8 = 16
* 4 * 4 = 16

### Answer: (1, 16), (2, 8), (4, 4) 

Expected answer: [(1, 16), (2, 8), (4, 4)]

Correct? Yes

Problem: Find all the factor pairs of the number 21.

Gemini-1.5 Pro:

Reasoning: Factor pairs are the numbers you multiply together to get another number. 

Let's find all the factor pairs of 21:

* 1 × 21 = 21
* 3 × 7 = 21 

### Answer: (1, 21), (3, 7) 

Expected answer: [(1, 21), (3, 7)]

Correct? Yes

Problem: Could you determine all the factor pairs of 72?

Gemini-1.5 Pro:

To find all the factor pairs of 72, we need to find all the pairs of numbers that multiply together to give 72. 

* **Start with 1:** 1 x 72 = 72
* **Check 2:** 2 x 36 = 72
* **Check 3:** 3 x 24 = 72
* **Check 4:** 4 x 18 = 72
* **Check 6:** 6 x 12 = 72
* **Check 8:** 8 x 9 = 72

### Answer: The factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). 

Expected answer: [(1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)]

Correct? Yes

Problem: Determine all the factor pairs of 38.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are pairs of numbers which, when multiplied together, result in the given number. Let's list them systematically:
* 1 and 38 (because 1 x 38 = 38)
* 2 and 19 (because 2 x 19 = 38)

### Answer: (1, 38), (2, 19)

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

Problem: List all the factor pairs of 94.

Gemini-1.5 Pro:

Reasoning:  Factor pairs of 94 are the pairs of whole numbers that multiply together to give 94.
Let's list them systematically:

* 1 and 94:  1 * 94 = 94
* 2 and 47: 2 * 47 = 94 

Since 94 is not divisible by any other whole numbers, we have found all the factor pairs.

### Answer: (1, 94), (2, 47) 

Expected answer: [(1, 94), (2, 47)]

Correct? Yes

Problem: List all factor pairs of 32.

Gemini-1.5 Pro:

Reasoning: Factor pairs are numbers that multiply together to get the original number.
We can start with 1 and its pair, 32.
We continue in this fashion, finding that the factor pairs are (1,32), (2,16), and (4,8)
### Answer: (1,32), (2,16), (4,8) 

Expected answer: [(1, 32), (2, 16), (4, 8)]

Correct? No

Problem: Identify all factor pairs of the number 33.

Gemini-1.5 Pro:

A factor pair of a number is any two numbers that can be multiplied together to get that number.  

Since 33 is not divisible by 2, let's check divisibility by 3: 33 / 3 = 11

* 1 and 33 are a factor pair because 1 x 33 = 33
* 3 and 11 are a factor pair because 3 x 11 = 33

### Answer: (1, 33), (3, 11) 

Expected answer: [(1, 33), (3, 11)]

Correct? Yes

Problem: Write down all the factor pairs of 59.

Gemini-1.5 Pro:

59 is a prime number. A prime number has exactly two factors: 1 and itself.

Therefore, the factor pairs of 59 are:

1 x 59 = 59

### Answer: (1, 59) 

Expected answer: [(1, 59)]

Correct? Yes

Problem: List all the factor pairs of the number 54.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that when multiplied together equal the original number. Let's find all the factor pairs of 54.

* 1 × 54 = 54
* 2 × 27 = 54
* 3 × 18 = 54
* 6 × 9 = 54

### Answer: (1, 54), (2, 27), (3, 18), (6, 9) 

Expected answer: [(1, 54), (2, 27), (3, 18), (6, 9)]

Correct? Yes

Problem: Determine all factor pairs of the number 85.

Gemini-1.5 Pro:

Reasoning:  A factor pair of 85 is a pair of positive integers that, when multiplied together, equal 85.  Since 85 is not divisible by 2, 3, or 4, we will continue testing divisibility by larger prime numbers until we find a factor.  We find that 85 is divisible by 5, as 85 / 5 = 17.  Therefore, the factor pairs of 85 are 1 and 85, and 5 and 17.

### Answer: (1, 85), (5, 17) 

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

Problem: Identify all the factor pairs of the number 56.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are any two numbers that, when multiplied together, equal the original number. Let's find all the factors of 56 and pair them up.

* 1 and 56 (1 x 56 = 56)
* 2 and 28 (2 x 28 = 56)
* 4 and 14 (4 x 14 = 56)
* 7 and 8 (7 x 8 = 56)

### Answer: (1, 56), (2, 28), (4, 14), (7, 8) 

Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]

Correct? Yes

Problem: List all the factor pairs of the number 24.

Gemini-1.5 Pro:

A factor pair of 24 is two whole numbers that when multiplied together produce 24. Here is the list of factor pairs:

* 1 and 24
* 2 and 12
* 3 and 8
* 4 and 6

### Answer: (1, 24), (2, 12), (3, 8), (4, 6) 

Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]

Correct? Yes

Problem: What are all the factor pairs of the number 84?

Gemini-1.5 Pro:

Reasoning: Factor pairs are the pairs of numbers that when multiplied together, equal the original number. Let's find all the factors of 84 and pair them up:

* 1 and 84 (1 x 84 = 84)
* 2 and 42 (2 x 42 = 84)
* 3 and 28 (3 x 28 = 84)
* 4 and 21 (4 x 21 = 84)
* 6 and 14 (6 x 14 = 84)
* 7 and 12 (7 x 12 = 84) 

### Answer: (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12) 

Expected answer: [(1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12)]

Correct? Yes

Problem: Identify all factor pairs of the number 36.

Gemini-1.5 Pro:

To find all the factor pairs of 36, we need to think of all the numbers that divide evenly into 36. 

Here's the list of factor pairs:

* 1 and 36 (because 1 x 36 = 36)
* 2 and 18 (because 2 x 18 = 36)
* 3 and 12 (because 3 x 12 = 36)
* 4 and 9 (because 4 x 9 = 36)
* 6 and 6 (because 6 x 6 = 36)

### Answer: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) 

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

Problem: What are all the factor pairs of 85?

Gemini-1.5 Pro:

Reasoning: 85 is an odd number. The factors of 85 are the numbers that divide evenly into 85. 
The factor pairs of 85 are: 1 and 85, 5 and 17. 
### Answer: (1, 85), (5, 17) 

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

Problem: Identify all factor pairs of the number 34.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that multiply to create the original number. Let's go through the possibilities, starting with 1:

* 1 * 34 = 34
* 2 * 17 = 34

Since there are no other numbers that divide evenly into 34, we have found all the factor pairs.

### Answer: (1, 34), (2, 17) 

Expected answer: [(1, 34), (2, 17)]

Correct? Yes

Problem: Determine all factor pairs of 88.

Gemini-1.5 Pro:

Reasoning: We will start from 1 and go up to the nearest integer less than or equal to the square root of 88 (which is slightly less than 10) to find one number in the factor pair, and then we will divide 88 by that number to find the other number in the factor pair.

$1\times88=88$
$2\times44=88$
$4\times22=88$
$8\times11=88$

### Answer: (1, 88), (2, 44), (4, 22), (8, 11) 

Expected answer: [(1, 88), (2, 44), (4, 22), (8, 11)]

Correct? Yes

Problem: Write down all factor pairs for the number 83.

Gemini-1.5 Pro:

Reasoning: A factor pair of a number is two factors that, when multiplied, give the original number. Since 83 is a prime number, it only has two factors: 1 and itself. 
### Answer: (1, 83)

Expected answer: [(1, 83)]

Correct? Yes

Problem: What are all the factor pairs of 60?

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of whole numbers that multiply together to give us 60. 
Let's start with 1: 1 x 60 = 60
Then 2: 2 x 30 = 60
Then 3: 3 x 20 = 60
Then 4: 4 x 15 = 60
Then 5: 5 x 12 = 60
Then 6: 6 x 10 = 60
Finally: 10 x 6 = 60, but we already have that pair. 

### Answer: (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) 

Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]

Correct? Yes

Problem: Write down all factor pairs of 58.

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of numbers that multiply together to give 58. 
* We know that 1 and 58 are factors of 58, as any number is divisible by 1 and itself.
* 58 is even, so it's also divisible by 2. 58 divided by 2 is 29.

There are no other factors of 58.
### Answer: (1, 58), (2, 29) 
 

Expected answer: [(1, 58), (2, 29)]

Correct? Yes

Problem: Please list all of the factor pairs of the number 40.

Gemini-1.5 Pro:

Here are the factor pairs of 40:

* **1 and 40:**  1 x 40 = 40
* **2 and 20:**  2 x 20 = 40
* **4 and 10:**  4 x 10 = 40
* **5 and 8:**  5 x 8 = 40 

Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]

Correct? No

Problem: Identify all the factor pairs of 91.

Gemini-1.5 Pro:

Reasoning:  A factor pair of 91 is any two whole numbers that, when multiplied, equal 91. Let's find them:

* **1 and 91:**  1 * 91 = 91
* **7 and 13:** 7 * 13 = 91

### Answer: (1, 91), (7, 13) 

Expected answer: [(1, 91), (7, 13)]

Correct? Yes

Problem: List all the factor pairs of 76.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are numbers that multiply together to get the original number.  We will start with 1 and its pair and continue until we reach the middle pairs.

* 1 x 76 = 76
* 2 x 38 = 76
* 4 x 19 = 76

### Answer: (1, 76), (2, 38), (4, 19) 

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

Problem: What are all the factor pairs of 13?

Gemini-1.5 Pro:

Reasoning: A factor pair of 13 is any two whole numbers that multiply to give 13. 13 is a prime number, which means its only factors are 1 and itself.
### Answer: (1, 13) 

Expected answer: [(1, 13)]

Correct? Yes

Problem: Find all factor pairs of 64.

Gemini-1.5 Pro:

Reasoning:  We need to find all the pairs of whole numbers that multiply together to give us 64.

* 1 and 64 ( 1 x 64 = 64)
* 2 and 32 ( 2 x 32 = 64)
* 4 and 16 ( 4 x 16 = 64)
* 8 and 8  ( 8 x 8  = 64)

### Answer: (1, 64), (2, 32), (4, 16), (8, 8)
 

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? Yes

Problem: What are all factor pairs of 8?

Gemini-1.5 Pro:

A factor pair of 8 consists of two numbers that, when multiplied together, equal 8. Here is the complete list:

* 1 x 8 = 8
* 2 x 4 = 8 

### Answer: (1, 8), (2, 4) 

Expected answer: [(1, 8), (2, 4)]

Correct? Yes

Problem: List all the factor pairs of 80.

Gemini-1.5 Pro:

Reasoning: Factor pairs of 80 are any two numbers that, when multiplied together, equal 80.  Let's list them systematically:

* 1 and 80 (1 x 80 = 80)
* 2 and 40 (2 x 40 = 80)
* 4 and 20 (4 x 20 = 80)
* 5 and 16 (5 x 16 = 80)
* 8 and 10 (8 x 10 = 80)

### Answer: (1, 80), (2, 40), (4, 20), (5, 16), (8, 10) 

Expected answer: [(1, 80), (2, 40), (4, 20), (5, 16), (8, 10)]

Correct? Yes

Problem: Calculate all the factor pairs for the number 96.

Gemini-1.5 Pro:

Reasoning: 
*  Factor pairs are numbers that, when multiplied, give you the original number. 
*  We start with 1 and the number itself (96) and then check divisibility by 2, 3, 4, and so on.

Here are the factor pairs of 96:
* 1 and 96 (1 x 96 = 96)
* 2 and 48 (2 x 48 = 96)
* 3 and 32 (3 x 32 = 96)
* 4 and 24 (4 x 24 = 96)
* 6 and 16 (6 x 16 = 96)
* 8 and 12 (8 x 12 = 96)

### Answer: (1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12) 

Expected answer: [(1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12)]

Correct? Yes

Problem: Calculate all factor pairs of 19.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are the numbers that divide evenly into that number. 19 is a prime number, which means its only factors are 1 and itself. 
Therefore the only factor pair for 19 is 1 and 19. 
### Answer: (1, 19)

Expected answer: [(1, 19)]

Correct? Yes

Problem: What are all factor pairs of 37?

Gemini-1.5 Pro:

Reasoning: The number 37 is a prime number. A prime number has exactly two factors: 1 and itself.
### Answer: 1 and 37. 

Expected answer: [(1, 37)]

Correct? Yes

Problem: Write down all factor pairs of the number 6.

Gemini-1.5 Pro:

The factor pairs of 6 are:

* 1 and 6 (because 1 x 6 = 6)
* 2 and 3 (because 2 x 3 = 6) 

Expected answer: [(1, 6), (2, 3)]

Correct? No

Problem: List down all the factor pairs of 58.

Gemini-1.5 Pro:

Reasoning: Factor pairs of 58 are the pairs of whole numbers which when multiplied together produce 58. Let's find all the factors of 58: 1, 2, 29, 58.

Here are the factor pairs of 58:
1 × 58
2 × 29
 
### Answer: (1, 58), (2, 29) 

Expected answer: [(1, 58), (2, 29)]

Correct? Yes

Problem: List all the factor pairs of the number 81.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are any two numbers that multiply together to make a specific number. Let's find all the factors of 81 and then list them as pairs:

* 1 and 81 (1 x 81 = 81)
* 3 and 27 (3 x 27 = 81)
* 9 and 9 (9 x 9 = 81) 

### Answer: (1, 81), (3, 27), (9, 9) 

Expected answer: [(1, 81), (3, 27), (9, 9)]

Correct? Yes

Problem: Please list all factor pairs of the number 85.

Gemini-1.5 Pro:

Reasoning: A factor pair of 85 is any two whole numbers that multiply together to give 85.  We can start at 1 and work our way up to find all of them:
* 1 x 85 = 85
* 5 x 17 = 85

### Answer: (1, 85), (5, 17) 

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

Problem: Write down all factor pairs for the number 93.

Gemini-1.5 Pro:

Reasoning:
We need to find all the pairs of whole numbers that multiply together to give us 93.

* 1 and 93 are factors of 93 because 1 x 93 = 93
* 3 and 31 are factors of 93 because 3 x 31 = 93

### Answer: (1, 93), (3, 31)

Expected answer: [(1, 93), (3, 31)]

Correct? Yes

Problem: Identify all factor pairs of 24.

Gemini-1.5 Pro:

Reasoning: 
A factor pair of 24 is any two whole numbers that multiply together to give us 24. Let's find all the factor pairs systematically:

* **1 and 24:** 1 x 24 = 24
* **2 and 12:** 2 x 12 = 24
* **3 and 8:** 3 x 8 = 24
* **4 and 6:** 4 x 6 = 24 

### Answer: (1, 24), (2, 12), (3, 8), (4, 6) 

Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]

Correct? Yes

Problem: List all the factor pairs of 97.

Gemini-1.5 Pro:

Reasoning: The only factors of 97 are 1 and itself because it is a prime number. 
### Answer: (1, 97) 

Expected answer: [(1, 97)]

Correct? Yes

Problem: Identify all factor pairs of the number 57.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that can be multiplied together to get the original number. Let's find all the factors of 57 and pair them up:

* 1 and 57 (1 x 57 = 57)
* 3 and 19 (3 x 19 = 57)

### Answer: (1, 57), (3, 19) 

Expected answer: [(1, 57), (3, 19)]

Correct? Yes

Problem: List down all the factor pairs of 19.

Gemini-1.5 Pro:

Reasoning: A factor pair of 19 is two whole numbers that, when multiplied, result in 19.  The only factor pairs of 19 are 1 and 19 because it is a prime number. 
### Answer: 1 and 19 

Expected answer: [(1, 19)]

Correct? Yes

Problem: What are all factor pairs of 38?

Gemini-1.5 Pro:

Reasoning: Factor pairs of 38 are the two whole numbers that multiply to produce 38. 
They are:
* 1 and 38 (because 1 x 38 = 38)
* 2 and 19 (because 2 x 19 = 38)

### Answer: (1, 38), (2, 19) 

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

Problem: Find all the factor pairs of the number 6.

Gemini-1.5 Pro:

Reasoning: The factors of 6 are the numbers that divide evenly into 6. 
* 1 and 6 are factors of 6 because 1 x 6 = 6.
* 2 and 3 are factors of 6 because 2 x 3 = 6.

### Answer: (1, 6), (2, 3) 

Expected answer: [(1, 6), (2, 3)]

Correct? Yes

Problem: Write down all factor pairs of 17.

Gemini-1.5 Pro:

The only factors of 17 are 1 and 17. 

### Answer: (1, 17) 

Expected answer: [(1, 17)]

Correct? Yes

Problem: List all factor pairs of 45.

Gemini-1.5 Pro:

Reasoning: Factor pairs of 45 are the pairs of numbers that multiply together to equal 45.
Here are the factor pairs:
1 x 45 = 45
3 x 15 = 45
5 x 9 = 45

### Answer: (1, 45), (3, 15), (5, 9) 

Expected answer: [(1, 45), (3, 15), (5, 9)]

Correct? Yes

Problem: Write down all factor pairs of 36.

Gemini-1.5 Pro:

A factor pair of 36 is any two whole numbers that multiply to give 36. Here's the list:

* 1 and 36 
* 2 and 18
* 3 and 12
* 4 and 9
* 6 and 6 

### Answer: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) 

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

Problem: What are all factor pairs of 89?

Gemini-1.5 Pro:

Reasoning: A factor pair for a number is two whole numbers that multiply to produce that number. 89 is a prime number, meaning it can only be divided evenly by 1 and itself. 

### Answer: 1 and 89 

Expected answer: [(1, 89)]

Correct? Yes

Problem: List all the factor pairs of 89.

Gemini-1.5 Pro:

Reasoning: A factor pair of 89 is any two whole numbers that multiply to give 89. Since 89 is a prime number, it only has two factors: 1 and itself.

### Answer: (1, 89) 

Expected answer: [(1, 89)]

Correct? Yes

Problem: List all the factor pairs of the number 44.

Gemini-1.5 Pro:

The factor pairs of a number are the pairs of numbers that multiply together to give the original number. Here are the factor pairs of 44:

* 1 and 44 (1 x 44 = 44)
* 2 and 22 (2 x 22 = 44)
* 4 and 11 (4 x 11 = 44)

### Answer: (1, 44), (2, 22), (4, 11) 

Expected answer: [(1, 44), (2, 22), (4, 11)]

Correct? Yes

Problem: Identify all factor pairs of the number 36.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are any two numbers that divide evenly into that number. We can find all factor pairs of 36 by listing out all the numbers that divide evenly into 36, starting from 1 and going up to the square root of 36, which is 6. For each factor we find less than or equal to 6, there will be a corresponding factor greater than or equal to 6. 

* 1 x 36 = 36
* 2 x 18 = 36
* 3 x 12 = 36
* 4 x 9 = 36
* 6 x 6 = 36

### Answer: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

Problem: List all possible factor pairs of the number 35.

Gemini-1.5 Pro:

A factor pair of a number is two numbers that when multiplied together equal the original number. Here's how to find all the factor pairs of 35:

* **Start with 1:** 1 x 35 = 35
* **Check divisibility by 5:** 5 x 7 = 35
* **Since 35 is not even, it's not divisible by 2 or any other even number.**
* **Try 3, but it doesn't divide evenly into 35.**
* **We've already found 7, so we don't need to check higher numbers.**

### Answer: (1, 35), (5, 7) 

Expected answer: [(1, 35), (5, 7)]

Correct? Yes

Problem: Write down all factor pairs of 22.

Gemini-1.5 Pro:

Reasoning: A factor pair of 22 is two whole numbers that when multiplied result in 22.
22 = 1 * 22
22 = 2 * 11
### Answer: (1, 22), (2, 11) 

Expected answer: [(1, 22), (2, 11)]

Correct? Yes

Problem: Find all the factor pairs of 40.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are the numbers that you multiply together to get another number. We need to find all the pairs of numbers that multiply to give us 40.

* 1 x 40 = 40
* 2 x 20 = 40
* 4 x 10 = 40
* 5 x 8 = 40

### Answer: (1, 40), (2, 20), (4, 10), (5, 8) 

Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]

Correct? Yes

Problem: List all the factor pairs of the number 64.

Gemini-1.5 Pro:

Reasoning: Factor pairs are any two numbers that when multiplied together equal the original number. We will start with 1 and go up through the factors until we start repeating factor pairs.

* 1 * 64 = 64
* 2 * 32 = 64
* 4 * 16 = 64
* 8 * 8 = 64 

### Answer: (1, 64), (2, 32), (4, 16), (8, 8)

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? Yes

Problem: Determine all factor pairs of 30.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are any two numbers that divide evenly into that number. Let's find all the factors of 30 and then pair them up.

* 1 and 30 (1 x 30 = 30)
* 2 and 15 (2 x 15 = 30)
* 3 and 10 (3 x 10 = 30)
* 5 and 6  (5 x 6 = 30)

### Answer: (1, 30), (2, 15), (3, 10), (5, 6) 

Expected answer: [(1, 30), (2, 15), (3, 10), (5, 6)]

Correct? Yes

Problem: List all factor pairs of 59.

Gemini-1.5 Pro:

Reasoning: 59 is a prime number. A prime number has exactly two factors: 1 and itself.
### Answer: (1, 59) 

Expected answer: [(1, 59)]

Correct? Yes

Problem: List all factor pairs of 18.

Gemini-1.5 Pro:

A factor pair of 18 is any two whole numbers that, when multiplied, result in 18. Here's the list:

* 1 and 18 (1 x 18 = 18)
* 2 and 9  (2 x 9 = 18)
* 3 and 6  (3 x 6 = 18)

### Answer: (1, 18), (2, 9), (3, 6) 

Expected answer: [(1, 18), (2, 9), (3, 6)]

Correct? Yes

Problem: Please list all the factor pairs of 61.

Gemini-1.5 Pro:

61 is a prime number, which means its only factors are 1 and itself. 

### Answer: (1, 61) 

Expected answer: [(1, 61)]

Correct? Yes

Problem: What are all of the factor pairs of 86?

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of whole numbers that multiply together to give us 86.

* 1 and 86 are factors because 1 x 86 = 86
* 2 and 43 are factors because 2 x 43 = 86

There are no other whole numbers that divide evenly into 86.

### Answer: (1, 86), (2, 43) 

Expected answer: [(1, 86), (2, 43)]

Correct? Yes

Problem: List out all factor pairs of 57.

Gemini-1.5 Pro:

Reasoning: A factor pair of 57 is two whole numbers that when multiplied together equal 57. We will start with 1 and go up, checking what number when multiplied by our number equals 57.

* 1 x 57 = 57
* 3 x 19 = 57 

### Answer: (1, 57), (3, 19) 

Expected answer: [(1, 57), (3, 19)]

Correct? Yes

Problem: What are all factor pairs of 38?

Gemini-1.5 Pro:

Reasoning: A factor pair of 38 is any two whole numbers that, when multiplied together, equal 38. Let's find all the factor pairs:
* 1 and 38 (1 x 38 = 38)
* 2 and 19 (2 x 19 = 38) 

### Answer: (1, 38), (2, 19)

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

Problem: Please list all factor pairs of 27.

Gemini-1.5 Pro:

Reasoning:  Factor pairs are any two numbers that when multiplied result in the given number. 

Let's find all the factor pairs of 27:

* 1 x 27 = 27
* 3 x 9 = 27

### Answer: (1, 27), (3, 9)

Expected answer: [(1, 27), (3, 9)]

Correct? Yes

Problem: List all the factor pairs of the number 78.

Gemini-1.5 Pro:

We need to find all the pairs of numbers that multiply together to give 78.

* **1 and 78:**  1 * 78 = 78
* **2 and 39:**  2 * 39 = 78
* **3 and 26:**  3 * 26 = 78
* **6 and 13:**  6 * 13 = 78

### Answer: (1, 78), (2, 39), (3, 26), (6, 13) 

Expected answer: [(1, 78), (2, 39), (3, 26), (6, 13)]

Correct? Yes

Problem: List out all the factor pairs of 23.

Gemini-1.5 Pro:

Reasoning:  The only numbers that divide evenly into 23 are 1 and 23. 

### Answer: 1 and 23 

Expected answer: [(1, 23)]

Correct? Yes

Problem: List down all the factor pairs of 2.

Gemini-1.5 Pro:

The factors of a number are the numbers that divide evenly into that number.
 
 The factors of 2 are 1 and 2 because:
 
 * 1 x 2 = 2 
 
 Therefore, the factor pairs of 2 are:
 
 *  1 and 2
 ### Answer: (1, 2)
 
 
 

Expected answer: [(1, 2)]

Correct? Yes

Problem: Write down all the factor pairs of 49.

Gemini-1.5 Pro:

Reasoning: Factor pairs of a number are any two numbers that, when multiplied together, give the original number. Let's find all the factors of 49:
 
 * 1 and 49 (because 1 × 49 = 49)
 * 7 and 7 (because 7 × 7 = 49)
 
 ### Answer: (1, 49), (7, 7) 

Expected answer: [(1, 49), (7, 7)]

Correct? Yes

Problem: Identify all the distinct pairs of factors that can multiply to give the number 93.

Gemini-1.5 Pro:

Reasoning: We need to find all the pairs of numbers that multiply to give 93.  We'll start with 1 and go up:

* 1 x 93 = 93 
* 3 x 31 = 93

There are no other whole numbers that divide evenly into 93.

### Answer: (1, 93), (3, 31) 

Expected answer: [(1, 93), (3, 31)]

Correct? Yes