LLemma 34B on 4.OA.B.4
Common Core Standard 4.OA.B.4
This standard covers the following:
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Problem: Find all factor pairs of 64.
LLemma 34B:
Reasoning: 64 = 1*64 = 2*32 = 4*16 = 8*8 ### Answer: 1, 2, 4, 8, 16, 32, 64
Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]
Correct? Yes
Problem: List all the factor pairs of 18.
LLemma 34B:
Reasoning: 18 = 1*18 = 2*9 = 3*6 ### Answer: 1, 18; 2, 9; 3, 6
Expected answer: [(1, 18), (2, 9), (3, 6)]
Correct? Yes
Problem: Find all factor pairs of 28.
LLemma 34B:
Reasoning: 28 = 1*28 = 2*14 = 4*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.
LLemma 34B:
Reasoning: 48 = 1*48 = 2*24 = 3*16 = 4*12 = 6*8 ### 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.
LLemma 34B:
Reasoning: 7 is a prime number. ### Answer: 1 and 7
Expected answer: [(1, 7)]
Correct? Yes
Problem: Write down every pair of factors of 98.
LLemma 34B:
Reasoning: 98 = 2*49 = 1*98 2 and 49 are factors of 98. 1 and 98 are factors of 98. ### Answer: 2, 49, 1, 98
Expected answer: [(1, 98), (2, 49), (7, 14)]
Correct? No
Problem: List all the factor pairs of the number 26.
LLemma 34B:
Reasoning: The factor pairs of 26 are (1,26), (2,13), and (1,26). ### Answer: (1,26), (2,13), and (1,26)
Expected answer: [(1, 26), (2, 13)]
Correct? No
Problem: Write down all factor pairs of 59.
LLemma 34B:
Reasoning: 59 is a prime number. ### Answer: 1 and 59
Expected answer: [(1, 59)]
Correct? Yes
Problem: Find out all factor pairs of 20.
LLemma 34B:
Reasoning: 20 = 1*20 = 2*10 = 4*5 ### 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.
LLemma 34B:
Reasoning: 20 = 1*20 = 2*10 = 4*5 ### Answer: 1*20, 2*10, 4*5
Expected answer: [(1, 20), (2, 10), (4, 5)]
Correct? Yes
Problem: Please list down all factor pairs of 13.
LLemma 34B:
Reasoning: 13 is a prime number. ### Answer: 13
Expected answer: [(1, 13)]
Correct? No
Problem: Find all factor pairs of 81.
LLemma 34B:
Reasoning: 81 = 1*81 = 3*27 = 9*9 ### Answer: 1, 81; 3, 27; 9, 9
Expected answer: [(1, 81), (3, 27), (9, 9)]
Correct? Yes
Problem: List all factor pairs of 76.
LLemma 34B:
Reasoning: 76 = 1*76 = 2*38 = 4*19 ### 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.
LLemma 34B:
Reasoning: 50 = 1*50 = 2*25 = 5*10 ### 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.
LLemma 34B:
Reasoning: The factor pairs of 76 are (1,76), (2,38), (4,19), and (8,9). ### Answer: (1,76), (2,38), (4,19), and (8,9)
Expected answer: [(1, 76), (2, 38), (4, 19)]
Correct? No
Problem: List all factor pairs of 56.
LLemma 34B:
Reasoning: 56 = 1*56 = 2*28 = 4*14 = 7*8 ### Answer: 1, 2, 4, 7, 8, 14, 28, 56
Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]
Correct? Yes
Problem: List all the factor pairs of the number 44.
LLemma 34B:
Reasoning: The factor pairs of 44 are (1,44), (2,22), and (4,11). ### Answer: (1,44), (2,22), and (4,11)
Expected answer: [(1, 44), (2, 22), (4, 11)]
Correct? No
Problem: List all the factor pairs of 5.
LLemma 34B:
Reasoning: 5 = 1*5 = 5*1 5 = 2*2.5 = 2.5*2 5 = 5*1 = 1*5 ### Answer: 1, 5; 2, 2.5; 5, 1; 2.5, 2
Expected answer: [(1, 5)]
Correct? No
Problem: Identify all factor pairs of the number 95.
LLemma 34B:
Reasoning: 95 = 1*95 = 5*19 = 19*5 ### Answer: 1, 95; 5, 19; 19, 5
Expected answer: [(1, 95), (5, 19)]
Correct? Yes
Problem: Please list all the factor pairs of 36.
LLemma 34B:
Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*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.
LLemma 34B:
Reasoning: The factor pairs of 59 are (1,59), (59,1), (7,8), and (8,7). ### Answer: (1,59), (59,1), (7,8), and (8,7)
Expected answer: [(1, 59)]
Correct? No
Problem: What are all the factor pairs of 3?
LLemma 34B:
Reasoning: 3 is a prime number. ### Answer: 1 and 3
Expected answer: [(1, 3)]
Correct? Yes
Problem: Could you list all factor pairs of 51?
LLemma 34B:
Reasoning: 51 is a prime number. ### Answer: 1 and 51
Expected answer: [(1, 51), (3, 17)]
Correct? No
Problem: List all factor pairs of 50.
LLemma 34B:
Reasoning: 50 = 1*50 = 2*25 = 5*10 ### 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.
LLemma 34B:
Reasoning: 47 is a prime number. ### Answer: 1 and 47
Expected answer: [(1, 47)]
Correct? Yes
Problem: Write down all factor pairs of 51.
LLemma 34B:
Reasoning: 51 is a prime number. ### Answer: 1 and 51
Expected answer: [(1, 51), (3, 17)]
Correct? No
Problem: List all factor pairs of 60.
LLemma 34B:
Reasoning: 60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10 ### 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.
LLemma 34B:
Reasoning: 43 is a prime number. ### Answer: 1 and 43
Expected answer: [(1, 43)]
Correct? Yes
Problem: List all factor pairs of 70.
LLemma 34B:
Reasoning: 70 = 1*70 = 2*35 = 5*14 = 10*7 ### Answer: 1, 70; 2, 35; 5, 14; 10, 7
Expected answer: [(1, 70), (2, 35), (5, 14), (7, 10)]
Correct? Yes
Problem: Please list all the factors of the number 2.
LLemma 34B:
Reasoning: The factors of 2 are 1 and 2. ### Answer: 1 and 2
Expected answer: [(1, 2)]
Correct? Yes
Problem: List all the factor pairs of 49.
LLemma 34B:
Reasoning: 49 is a prime number. ### Answer: 1 and 49
Expected answer: [(1, 49), (7, 7)]
Correct? No
Problem: Identify all factor pairs of 17.
LLemma 34B:
Reasoning: 17 is a prime number. ### Answer: 17
Expected answer: [(1, 17)]
Correct? No
Problem: Find all the factor pairs of 35.
LLemma 34B:
Reasoning: 35 = 1*35 = 5*7 ### Answer: 1 and 35, 5 and 7
Expected answer: [(1, 35), (5, 7)]
Correct? Yes
Problem: Identify all factor pairs of the number 91.
LLemma 34B:
Reasoning: 91 is a prime number. ### Answer: 1 and 91
Expected answer: [(1, 91), (7, 13)]
Correct? No
Problem: List all factor pairs of the number 97.
LLemma 34B:
Reasoning: 97 is a prime number. ### Answer: 1 and 97
Expected answer: [(1, 97)]
Correct? Yes
Problem: What are all the factor pairs of 16?
LLemma 34B:
Reasoning: 16 = 1*16 = 2*8 = 4*4 ### 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.
LLemma 34B:
Reasoning: The factor pairs of 21 are (1,21), (3,7). ### Answer: (1,21), (3,7)
Expected answer: [(1, 21), (3, 7)]
Correct? No
Problem: Could you determine all the factor pairs of 72?
LLemma 34B:
Reasoning: The factor pairs of 72 are (1,72), (2,36), (3,24), (4,18), (6,12), and (8,9). ### Answer: (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? No
Problem: Determine all the factor pairs of 38.
LLemma 34B:
Reasoning: 38 = 1*38 = 2*19 = 19*2 ### Answer: 1, 38; 2, 19; 19, 2
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: List all the factor pairs of 94.
LLemma 34B:
Reasoning: 94 = 2*47 = 1*94 The factor pairs of 94 are (1,94), (2,47). ### Answer: (1,94), (2,47)
Expected answer: [(1, 94), (2, 47)]
Correct? No
Problem: List all factor pairs of 32.
LLemma 34B:
Reasoning: 32 = 1*32 = 2*16 = 4*8 = 8*4 = 16*2 = 32*1 ### Answer: 1, 32; 2, 16; 4, 8; 8, 4; 16, 2; 32, 1
Expected answer: [(1, 32), (2, 16), (4, 8)]
Correct? Yes
Problem: Identify all factor pairs of the number 33.
LLemma 34B:
Reasoning: 33 = 1*33 = 3*11 ### Answer: 1 and 33, 3 and 11
Expected answer: [(1, 33), (3, 11)]
Correct? Yes
Problem: Write down all the factor pairs of 59.
LLemma 34B:
Reasoning: 59 is a prime number. ### Answer: 1 and 59
Expected answer: [(1, 59)]
Correct? Yes
Problem: List all the factor pairs of the number 54.
LLemma 34B:
Reasoning: The factor pairs of 54 are (1,54), (2,27), (3,18), (6,9). ### Answer: (1,54), (2,27), (3,18), (6,9)
Expected answer: [(1, 54), (2, 27), (3, 18), (6, 9)]
Correct? No
Problem: Determine all factor pairs of the number 85.
LLemma 34B:
Reasoning: 85 = 1*85 = 5*17 ### Answer: 1 and 85, 5 and 17
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Identify all the factor pairs of the number 56.
LLemma 34B:
Reasoning: The factor pairs of 56 are: 1 and 56 2 and 28 4 and 14 8 and 7 ### Answer: 1 and 56, 2 and 28, 4 and 14, 8 and 7
Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]
Correct? Yes
Problem: List all the factor pairs of the number 24.
LLemma 34B:
Reasoning: The factor pairs of 24 are (1,24), (2,12), (3,8), and (4,6). ### Answer: (1,24), (2,12), (3,8), and (4,6)
Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]
Correct? No
Problem: What are all the factor pairs of the number 84?
LLemma 34B:
Reasoning: The factor pairs of 84 are: 1 and 84, 2 and 42, 3 and 28, 4 and 21, 6 and 14, 7 and 12. ### Answer: 1 and 84, 2 and 42, 3 and 28, 4 and 21, 6 and 14, 7 and 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.
LLemma 34B:
Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6 ### Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]
Correct? Yes
Problem: What are all the factor pairs of 85?
LLemma 34B:
Reasoning: 85 = 1*85 = 5*17 ### Answer: 1 and 85, 5 and 17
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Identify all factor pairs of the number 34.
LLemma 34B:
Reasoning: 34 = 1*34 = 2*17 = 1*34 = 2*17 ### Answer: 1, 34; 2, 17
Expected answer: [(1, 34), (2, 17)]
Correct? Yes
Problem: Determine all factor pairs of 88.
LLemma 34B:
Reasoning: 88 = 1*88 = 2*44 = 4*22 = 8*11 ### Answer: 1, 2, 4, 8, 11, 22, 44, 88
Expected answer: [(1, 88), (2, 44), (4, 22), (8, 11)]
Correct? Yes
Problem: Write down all factor pairs for the number 83.
LLemma 34B:
Reasoning: 83 is a prime number. ### Answer: 1 and 83
Expected answer: [(1, 83)]
Correct? Yes
Problem: What are all the factor pairs of 60?
LLemma 34B:
Reasoning: 60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10 ### 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.
LLemma 34B:
Reasoning: 58 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2
Expected answer: [(1, 58), (2, 29)]
Correct? Yes
Problem: Please list all of the factor pairs of the number 40.
LLemma 34B:
Reasoning: The factor pairs of 40 are: 1 and 40, 2 and 20, 4 and 10, and 5 and 8. ### Answer: 1 and 40, 2 and 20, 4 and 10, and 5 and 8
Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]
Correct? Yes
Problem: Identify all the factor pairs of 91.
LLemma 34B:
Reasoning: 91 is a prime number. ### Answer: 1 and 91
Expected answer: [(1, 91), (7, 13)]
Correct? No
Problem: List all the factor pairs of 76.
LLemma 34B:
Reasoning: 76 = 1*76 = 2*38 = 4*19 = 7*11 ### Answer: 1, 76; 2, 38; 4, 19; 7, 11
Expected answer: [(1, 76), (2, 38), (4, 19)]
Correct? No
Problem: What are all the factor pairs of 13?
LLemma 34B:
Reasoning: 13 is a prime number. ### Answer: 1 and 13
Expected answer: [(1, 13)]
Correct? Yes
Problem: Find all factor pairs of 64.
LLemma 34B:
Reasoning: 64 = 1*64 = 2*32 = 4*16 = 8*8 ### Answer: 1, 2, 4, 8, 16, 32, 64
Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]
Correct? Yes
Problem: What are all factor pairs of 8?
LLemma 34B:
Reasoning: 8 = 1*8 = 2*4 ### Answer: 1, 8; 2, 4
Expected answer: [(1, 8), (2, 4)]
Correct? Yes
Problem: List all the factor pairs of 80.
LLemma 34B:
Reasoning: 80 = 1*80 = 2*40 = 4*20 = 5*16 = 8*10 ### 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.
LLemma 34B:
Reasoning: The factor pairs for 96 are: 1 and 96 2 and 48 3 and 32 4 and 24 6 and 16 8 and 12 ### Answer: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12
Expected answer: [(1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12)]
Correct? Yes
Problem: Calculate all factor pairs of 19.
LLemma 34B:
Reasoning: 19 is a prime number. ### Answer: 1 and 19
Expected answer: [(1, 19)]
Correct? Yes
Problem: What are all factor pairs of 37?
LLemma 34B:
Reasoning: 37 is a prime number. ### Answer: 1 and 37
Expected answer: [(1, 37)]
Correct? Yes
Problem: Write down all factor pairs of the number 6.
LLemma 34B:
Reasoning: 6 = 1*6 = 2*3 ### Answer: 1,6; 2,3
Expected answer: [(1, 6), (2, 3)]
Correct? No
Problem: List down all the factor pairs of 58.
LLemma 34B:
Reasoning: 58 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2*29 = 1*58 = 2
Expected answer: [(1, 58), (2, 29)]
Correct? Yes
Problem: List all the factor pairs of the number 81.
LLemma 34B:
Reasoning: 81 = 1*81 = 3*27 = 9*9 ### 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.
LLemma 34B:
Reasoning: 85 = 1*85 = 5*17 ### Answer: 1, 85; 5, 17
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Write down all factor pairs for the number 93.
LLemma 34B:
Reasoning: 93 = 1*93 = 3*31 = 9*11 ### Answer: 1, 93; 3, 31; 9, 11
Expected answer: [(1, 93), (3, 31)]
Correct? No
Problem: Identify all factor pairs of 24.
LLemma 34B:
Reasoning: 24 = 1*24 = 2*12 = 3*8 = 4*6 ### 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.
LLemma 34B:
Reasoning: 97 is a prime number. ### Answer: 1 and 97
Expected answer: [(1, 97)]
Correct? Yes
Problem: Identify all factor pairs of the number 57.
LLemma 34B:
Reasoning: 57 is a prime number. ### Answer: 1 and 57
Expected answer: [(1, 57), (3, 19)]
Correct? No
Problem: List down all the factor pairs of 19.
LLemma 34B:
Reasoning: 19 is a prime number. ### Answer: 1 and 19
Expected answer: [(1, 19)]
Correct? Yes
Problem: What are all factor pairs of 38?
LLemma 34B:
Reasoning: 38 = 1*38 = 2*19 = 19*2 ### Answer: 1, 38; 2, 19; 19, 2
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: Find all the factor pairs of the number 6.
LLemma 34B:
Reasoning: The factor pairs of 6 are (1,6) and (2,3). ### Answer: (1,6) and (2,3)
Expected answer: [(1, 6), (2, 3)]
Correct? No
Problem: Write down all factor pairs of 17.
LLemma 34B:
Reasoning: 17 is a prime number. ### Answer: 17
Expected answer: [(1, 17)]
Correct? No
Problem: List all factor pairs of 45.
LLemma 34B:
Reasoning: 45 = 1*45 = 3*15 = 5*9 ### 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.
LLemma 34B:
Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*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?
LLemma 34B:
Reasoning: 89 is a prime number. ### Answer: 1 and 89
Expected answer: [(1, 89)]
Correct? Yes
Problem: List all the factor pairs of 89.
LLemma 34B:
Reasoning: 89 is a prime number. ### Answer: 1 and 89
Expected answer: [(1, 89)]
Correct? Yes
Problem: List all the factor pairs of the number 44.
LLemma 34B:
Reasoning: The factor pairs of 44 are (1,44), (2,22), and (4,11). ### Answer: (1,44), (2,22), and (4,11)
Expected answer: [(1, 44), (2, 22), (4, 11)]
Correct? No
Problem: Identify all factor pairs of the number 36.
LLemma 34B:
Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6 ### Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]
Correct? Yes
Problem: List all possible factor pairs of the number 35.
LLemma 34B:
Reasoning: 35 = 1*35 = 5*7 ### Answer: 1, 35, 5, 7
Expected answer: [(1, 35), (5, 7)]
Correct? Yes
Problem: Write down all factor pairs of 22.
LLemma 34B:
Reasoning: 22 = 2*11 = 1*22. ### Answer: 1, 22; 2, 11
Expected answer: [(1, 22), (2, 11)]
Correct? Yes
Problem: Find all the factor pairs of 40.
LLemma 34B:
Reasoning: The factor pairs of 40 are (1,40), (2,20), (4,10), and (5,8). ### Answer: (1,40), (2,20), (4,10), and (5,8)
Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]
Correct? No
Problem: List all the factor pairs of the number 64.
LLemma 34B:
Reasoning: 64 = 1*64 = 2*32 = 4*16 = 8*8 ### 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.
LLemma 34B:
Reasoning: 30 = 1*30 = 2*15 = 3*10 = 5*6 ### 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.
LLemma 34B:
Reasoning: 59 is a prime number. ### Answer: 1 and 59
Expected answer: [(1, 59)]
Correct? Yes
Problem: List all factor pairs of 18.
LLemma 34B:
Reasoning: 18 = 1*18 = 2*9 = 3*6 ### 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.
LLemma 34B:
Reasoning: 61 is a prime number. ### Answer: 1 and 61
Expected answer: [(1, 61)]
Correct? Yes
Problem: What are all of the factor pairs of 86?
LLemma 34B:
Reasoning: 86 = 1*86 = 2*43 = 4*21 = 7*12 ### Answer: 1, 86; 2, 43; 4, 21; 7, 12
Expected answer: [(1, 86), (2, 43)]
Correct? No
Problem: List out all factor pairs of 57.
LLemma 34B:
Reasoning: 57 is a prime number. ### Answer: 1 and 57
Expected answer: [(1, 57), (3, 19)]
Correct? No
Problem: What are all factor pairs of 38?
LLemma 34B:
Reasoning: 38 = 1*38 = 2*19 = 19*2 ### Answer: 1, 38; 2, 19; 19, 2
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: Please list all factor pairs of 27.
LLemma 34B:
Reasoning: 27 = 1*27 = 3*9 = 9*3 = 3*3*3 ### Answer: 1, 3, 9, 27
Expected answer: [(1, 27), (3, 9)]
Correct? Yes
Problem: List all the factor pairs of the number 78.
LLemma 34B:
Reasoning: 78 = 1*78 = 2*39 = 6*13 ### Answer: 1, 78; 2, 39; 6, 13
Expected answer: [(1, 78), (2, 39), (3, 26), (6, 13)]
Correct? No
Problem: List out all the factor pairs of 23.
LLemma 34B:
Reasoning: 23 is a prime number. ### Answer: 1 and 23
Expected answer: [(1, 23)]
Correct? Yes
Problem: List down all the factor pairs of 2.
LLemma 34B:
Reasoning: The factor pairs of 2 are (1,2) and (2,1). ### Answer: (1,2) and (2,1)
Expected answer: [(1, 2)]
Correct? No
Problem: Write down all the factor pairs of 49.
LLemma 34B:
Reasoning: 49 is a prime number. ### Answer: 1 and 49
Expected answer: [(1, 49), (7, 7)]
Correct? No
Problem: Identify all the distinct pairs of factors that can multiply to give the number 93.
LLemma 34B:
Reasoning: 93 = 1*93 = 3*31 = 9*13 ### Answer: 1, 93; 3, 31; 9, 13
Expected answer: [(1, 93), (3, 31)]
Correct? No