InternLM-Math Base 20B 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.
InternLM-Math Base 20B:
Reasoning: 64 = 2*2*2*2*2*2 = 2^6 The factor pairs of 64 are: (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? No
Problem: List all the factor pairs of 18.
InternLM-Math Base 20B:
Reasoning: 18 = 1 x 18 = 2 x 9 = 3 x 6 The factor pairs of 18 are (1, 18), (2, 9), and (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.
InternLM-Math Base 20B:
Reasoning: 28 = 2 × 14 = 4 × 7 = 7 × 4 = 14 × 2 = 28 × 1. ### Answer: 2 × 14, 4 × 7, 7 × 4, 14 × 2, 28 × 1
Expected answer: [(1, 28), (2, 14), (4, 7)]
Correct? Yes
Problem: List all factor pairs of the number 48.
InternLM-Math Base 20B:
Reasoning: 48 = 2 × 2 × 2 × 2 × 3. The factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), and (8, 6). ### Answer: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), and (8, 6)
Expected answer: [(1, 48), (2, 24), (3, 16), (4, 12), (6, 8)]
Correct? Yes
Problem: Write down all factor pairs of 7.
InternLM-Math Base 20B:
Reasoning: 7 = 1 x 7 7 = 7 x 1 ### Answer: 1 x 7, 7 x 1
Expected answer: [(1, 7)]
Correct? Yes
Problem: Write down every pair of factors of 98.
InternLM-Math Base 20B:
Reasoning: 98 = 2 × 49 = 7 × 14 ### Answer: 2 × 49, 7 × 14
Expected answer: [(1, 98), (2, 49), (7, 14)]
Correct? No
Problem: List all the factor pairs of the number 26.
InternLM-Math Base 20B:
Reasoning: 26 = 1 x 26, 2 x 13. The factor pairs of 26 are (1, 26) and (2, 13). ### Answer: (1, 26) and (2, 13)
Expected answer: [(1, 26), (2, 13)]
Correct? Yes
Problem: Write down all factor pairs of 59.
InternLM-Math Base 20B:
Reasoning: 59 is a prime number. Therefore, the only factor pair of 59 is 1 and 59. ### Answer: 1 and 59
Expected answer: [(1, 59)]
Correct? Yes
Problem: Find out all factor pairs of 20.
InternLM-Math Base 20B:
Reasoning: 20 = 2*10 = 4*5 = 20*1 ### Answer: 2*10, 4*5, 20*1
Expected answer: [(1, 20), (2, 10), (4, 5)]
Correct? Yes
Problem: Write down all factor pairs of 20.
InternLM-Math Base 20B:
Reasoning: 20 = 1*20 = 2*10 = 4*5 The factor pairs of 20 are (1,20), (2,10), and (4,5). ### Answer: (1,20), (2,10), (4,5)
Expected answer: [(1, 20), (2, 10), (4, 5)]
Correct? No
Problem: Please list down all factor pairs of 13.
InternLM-Math Base 20B:
Reasoning: 13 is a prime number. It has only two factors, 1 and 13. ### Answer: 1 and 13
Expected answer: [(1, 13)]
Correct? Yes
Problem: Find all factor pairs of 81.
InternLM-Math Base 20B:
Reasoning: 81 = 9*9 = 3*3*3*3 = 3^4 81 has 5 factor pairs: (1,81), (3,27), (9,9), (27,3), (81,1) ### Answer: (1,81), (3,27), (9,9), (27,3), (81,1)
Expected answer: [(1, 81), (3, 27), (9, 9)]
Correct? No
Problem: List all factor pairs of 76.
InternLM-Math Base 20B:
Reasoning: 76 = 2 × 2 × 19. The factor pairs of 76 are (1, 76), (2, 38), (4, 19), and (76, 1). ### Answer: (1, 76), (2, 38), (4, 19), (76, 1)
Expected answer: [(1, 76), (2, 38), (4, 19)]
Correct? Yes
Problem: Write down all factor pairs of 50.
InternLM-Math Base 20B:
Reasoning: 50 = 1*50, 2*25, 5*10, 10*5, 25*2, 50*1 ### Answer: 1*50, 2*25, 5*10, 10*5, 25*2, 50*1
Expected answer: [(1, 50), (2, 25), (5, 10)]
Correct? Yes
Problem: List all the factor pairs of the number 76.
InternLM-Math Base 20B:
Reasoning: 76 = 2 x 2 x 19 The factor pairs of 76 are (1, 76), (2, 38), (4, 19), (19, 4), (38, 2), and (76, 1). ### Answer: (1, 76), (2, 38), (4, 19), (19, 4), (38, 2), (76, 1)
Expected answer: [(1, 76), (2, 38), (4, 19)]
Correct? Yes
Problem: List all factor pairs of 56.
InternLM-Math Base 20B:
Reasoning: 56 = 2 × 2 × 2 × 7 The factor pairs of 56 are (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7). ### Answer: (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7)
Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]
Correct? Yes
Problem: List all the factor pairs of the number 44.
InternLM-Math Base 20B:
Reasoning: 44 = 2 × 2 × 11 The factor pairs of 44 are (1, 44), (2, 22), (4, 11), and (44, 1). ### Answer: (1, 44), (2, 22), (4, 11), (44, 1)
Expected answer: [(1, 44), (2, 22), (4, 11)]
Correct? Yes
Problem: List all the factor pairs of 5.
InternLM-Math Base 20B:
Reasoning: 5 = 1 x 5 ### Answer: 1 x 5
Expected answer: [(1, 5)]
Correct? Yes
Problem: Identify all factor pairs of the number 95.
InternLM-Math Base 20B:
Reasoning: 95 = 5 × 19 95 = 1 × 95 95 = 5 × 19 95 = 1 × 95 ### Answer: 1 × 95, 5 × 19
Expected answer: [(1, 95), (5, 19)]
Correct? Yes
Problem: Please list all the factor pairs of 36.
InternLM-Math Base 20B:
Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6 The factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). ### Answer: (1, 36), (2, 18), (3, 12), (4, 9), and (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.
InternLM-Math Base 20B:
The factor pairs of 59 are: (1,59) and (59,1).
Expected answer: [(1, 59)]
Correct? No
Problem: What are all the factor pairs of 3?
InternLM-Math Base 20B:
Reasoning: 3 is a prime number, so it has only two factor pairs: 1×3 and 3×1. ### Answer: 1×3 and 3×1
Expected answer: [(1, 3)]
Correct? Yes
Problem: Could you list all factor pairs of 51?
InternLM-Math Base 20B:
Reasoning: 51 = 1 x 51, 3 x 17 ### Answer: 1 x 51, 3 x 17
Expected answer: [(1, 51), (3, 17)]
Correct? Yes
Problem: List all factor pairs of 50.
InternLM-Math Base 20B:
Reasoning: 50 = 1*50, 2*25, 5*10, 10*5, 25*2, 50*1 ### Answer: 1*50, 2*25, 5*10, 10*5, 25*2, 50*1
Expected answer: [(1, 50), (2, 25), (5, 10)]
Correct? Yes
Problem: Write down all factor pairs of 47.
InternLM-Math Base 20B:
Reasoning: 47 is a prime number. It has only two factors, 1 and 47. ### Answer: 1 and 47
Expected answer: [(1, 47)]
Correct? Yes
Problem: Write down all factor pairs of 51.
InternLM-Math Base 20B:
Reasoning: 51 = 1 x 51, 3 x 17 ### Answer: 1 x 51, 3 x 17
Expected answer: [(1, 51), (3, 17)]
Correct? Yes
Problem: List all factor pairs of 60.
InternLM-Math Base 20B:
Reasoning: 60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10 = 10*6 = 12*5 = 15*4 = 20*3 = 30*2 = 60*1 ### Answer: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1)
Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]
Correct? No
Problem: List all factor pairs of 43.
InternLM-Math Base 20B:
Reasoning: 43 is a prime number, so it has only two factor pairs: 1 and 43, and 43 and 1. ### Answer: 1 and 43, 43 and 1
Expected answer: [(1, 43)]
Correct? Yes
Problem: List all factor pairs of 70.
InternLM-Math Base 20B:
Reasoning: 70 = 2 × 5 × 7 The factor pairs of 70 are (1, 70), (2, 35), (5, 14), (7, 10), and (10, 7). ### Answer: (1, 70), (2, 35), (5, 14), (7, 10), and (10, 7)
Expected answer: [(1, 70), (2, 35), (5, 14), (7, 10)]
Correct? Yes
Problem: Please list all the factors of the number 2.
InternLM-Math Base 20B:
Reasoning: 2 is a prime number, so it has only two factors: 1 and 2. ### Answer: 1, 2
Expected answer: [(1, 2)]
Correct? Yes
Problem: List all the factor pairs of 49.
InternLM-Math Base 20B:
Reasoning: 49 = 1 x 49 = 7 x 7 ### Answer: 1 x 49, 7 x 7
Expected answer: [(1, 49), (7, 7)]
Correct? Yes
Problem: Identify all factor pairs of 17.
InternLM-Math Base 20B:
Reasoning: 17 is a prime number. Therefore, 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.
InternLM-Math Base 20B:
Reasoning: 35 = 5 × 7, so the factor pairs of 35 are (1, 35), (5, 7), (7, 5), and (35, 1). ### Answer: (1, 35), (5, 7), (7, 5), (35, 1)
Expected answer: [(1, 35), (5, 7)]
Correct? Yes
Problem: Identify all factor pairs of the number 91.
InternLM-Math Base 20B:
Reasoning: 91 = 7 × 13 91 = 1 × 91 ### Answer: 1 × 91, 7 × 13
Expected answer: [(1, 91), (7, 13)]
Correct? Yes
Problem: List all factor pairs of the number 97.
InternLM-Math Base 20B:
Reasoning: 97 is a prime number. The only factor pair of 97 is 1 and 97. ### Answer: 1 and 97
Expected answer: [(1, 97)]
Correct? Yes
Problem: What are all the factor pairs of 16?
InternLM-Math Base 20B:
Reasoning: 16 = 1 x 16 = 2 x 8 = 4 x 4 The factor pairs of 16 are (1, 16), (2, 8), and (4, 4). ### Answer: (1, 16), (2, 8), and (4, 4)
Expected answer: [(1, 16), (2, 8), (4, 4)]
Correct? Yes
Problem: Find all the factor pairs of the number 21.
InternLM-Math Base 20B:
Reasoning: 21 = 3 × 7. The factor pairs of 21 are (1, 21) and (3, 7). ### Answer: (1, 21) and (3, 7)
Expected answer: [(1, 21), (3, 7)]
Correct? Yes
Problem: Could you determine all the factor pairs of 72?
InternLM-Math Base 20B:
Reasoning: 72 = 2 × 2 × 2 × 3 × 3 The factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9). ### Answer: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (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.
InternLM-Math Base 20B:
Reasoning: 38 = 2 × 19. The factor pairs of 38 are (1, 38), (2, 19), and (38, 1). ### Answer: (1, 38), (2, 19), (38, 1)
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: List all the factor pairs of 94.
InternLM-Math Base 20B:
Reasoning: 94 = 2 x 47, so the factor pairs of 94 are (1, 94) and (2, 47). ### Answer: (1, 94) and (2, 47)
Expected answer: [(1, 94), (2, 47)]
Correct? Yes
Problem: List all factor pairs of 32.
InternLM-Math Base 20B:
Reasoning: 32 = 1 x 32, 2 x 16, 4 x 8, 8 x 4, 16 x 2, 32 x 1. ### Answer: 1 x 32, 2 x 16, 4 x 8, 8 x 4, 16 x 2, 32 x 1
Expected answer: [(1, 32), (2, 16), (4, 8)]
Correct? Yes
Problem: Identify all factor pairs of the number 33.
InternLM-Math Base 20B:
Reasoning: 33 = 3 × 11 33 = 1 × 33 ### Answer: 1 × 33, 3 × 11
Expected answer: [(1, 33), (3, 11)]
Correct? Yes
Problem: Write down all the factor pairs of 59.
InternLM-Math Base 20B:
Reasoning: 59 is a prime number. It has only two factors, 1 and 59. The only factor pair of 59 is (1, 59). ### Answer: (1, 59)
Expected answer: [(1, 59)]
Correct? Yes
Problem: List all the factor pairs of the number 54.
InternLM-Math Base 20B:
Reasoning: 54 = 2 x 3 x 3 x 3 The factor pairs of 54 are (1, 54), (2, 27), (3, 18), (6, 9), (9, 6), (18, 3), (27, 2), and (54, 1). ### Answer: (1, 54), (2, 27), (3, 18), (6, 9), (9, 6), (18, 3), (27, 2), and (54, 1)
Expected answer: [(1, 54), (2, 27), (3, 18), (6, 9)]
Correct? Yes
Problem: Determine all factor pairs of the number 85.
InternLM-Math Base 20B:
Reasoning: 85 = 5 × 17 The factor pairs of 85 are (1, 85), (5, 17), and (85, 1). ### Answer: (1, 85), (5, 17), and (85, 1)
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Identify all the factor pairs of the number 56.
InternLM-Math Base 20B:
Reasoning: 56 = 2 × 2 × 2 × 7 The factor pairs of 56 are (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7). ### Answer: (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7)
Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]
Correct? Yes
Problem: List all the factor pairs of the number 24.
InternLM-Math Base 20B:
Reasoning: 24 = 1 x 24, 2 x 12, 3 x 8, 4 x 6. ### Answer: 1 x 24, 2 x 12, 3 x 8, 4 x 6
Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]
Correct? Yes
Problem: What are all the factor pairs of the number 84?
InternLM-Math Base 20B:
Reasoning: 84 = 2 × 2 × 3 × 7 The factor pairs of 84 are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12), (12, 7), (14, 6), (21, 4), (28, 3), (42, 2), and (84, 1). ### Answer: (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12), (12, 7), (14, 6), (21, 4), (28, 3), (42, 2), and (84, 1)
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.
InternLM-Math Base 20B:
Reasoning: 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6. ### Answer: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6
Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]
Correct? Yes
Problem: What are all the factor pairs of 85?
InternLM-Math Base 20B:
Reasoning: 85 = 5 × 17 The factor pairs of 85 are (1, 85), (5, 17), (17, 5), and (85, 1). ### Answer: (1, 85), (5, 17), (17, 5), (85, 1)
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Identify all factor pairs of the number 34.
InternLM-Math Base 20B:
Reasoning: 34 = 2 x 17 The factor pairs of 34 are (1, 34) and (2, 17). ### Answer: (1, 34) and (2, 17)
Expected answer: [(1, 34), (2, 17)]
Correct? Yes
Problem: Determine all factor pairs of 88.
InternLM-Math Base 20B:
Reasoning: 88 = 2 × 2 × 2 × 11. The factor pairs of 88 are (1, 88), (2, 44), (4, 22), (8, 11), (11, 8), (22, 4), (44, 2), and (88, 1). ### Answer: (1, 88), (2, 44), (4, 22), (8, 11), (11, 8), (22, 4), (44, 2), (88, 1)
Expected answer: [(1, 88), (2, 44), (4, 22), (8, 11)]
Correct? Yes
Problem: Write down all factor pairs for the number 83.
InternLM-Math Base 20B:
Reasoning: 83 is a prime number. It has only two factors: 1 and 83. ### Answer: 1 and 83
Expected answer: [(1, 83)]
Correct? Yes
Problem: What are all the factor pairs of 60?
InternLM-Math Base 20B:
Reasoning: 60 = 2*2*3*5 The factor pairs of 60 are: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1) ### Answer: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1)
Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]
Correct? No
Problem: Write down all factor pairs of 58.
InternLM-Math Base 20B:
Reasoning: 58 = 1 x 58, 2 x 29, 58 x 1, 29 x 2. ### Answer: 1 x 58, 2 x 29, 58 x 1, 29 x 2
Expected answer: [(1, 58), (2, 29)]
Correct? Yes
Problem: Please list all of the factor pairs of the number 40.
InternLM-Math Base 20B:
Reasoning: 40 = 1*40 = 2*20 = 4*10 = 5*8 = 8*5 = 10*4 = 20*2 = 40*1 ### Answer: 1*40, 2*20, 4*10, 5*8, 8*5, 10*4, 20*2, 40*1
Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]
Correct? Yes
Problem: Identify all the factor pairs of 91.
InternLM-Math Base 20B:
Reasoning: 91 = 7 x 13 91 = 1 x 91 ### Answer: 1 x 91, 7 x 13
Expected answer: [(1, 91), (7, 13)]
Correct? Yes
Problem: List all the factor pairs of 76.
InternLM-Math Base 20B:
Reasoning: 76 = 2 x 38 = 4 x 19 = 1 x 76 The factor pairs of 76 are (2, 38), (4, 19), and (1, 76). ### Answer: (2, 38), (4, 19), and (1, 76)
Expected answer: [(1, 76), (2, 38), (4, 19)]
Correct? Yes
Problem: What are all the factor pairs of 13?
InternLM-Math Base 20B:
Reasoning: 13 is a prime number, so it has only two factor pairs: 1 and 13, and 13 and 1. ### Answer: 1 and 13, 13 and 1
Expected answer: [(1, 13)]
Correct? Yes
Problem: Find all factor pairs of 64.
InternLM-Math Base 20B:
Reasoning: 64 = 2*2*2*2*2*2 = 2^6 The factor pairs of 64 are: (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? No
Problem: What are all factor pairs of 8?
InternLM-Math Base 20B:
Reasoning: 8 = 1 × 8 = 2 × 4 The factor pairs of 8 are (1, 8) and (2, 4). ### Answer: (1, 8) and (2, 4)
Expected answer: [(1, 8), (2, 4)]
Correct? Yes
Problem: List all the factor pairs of 80.
InternLM-Math Base 20B:
Reasoning: 80 = 1*80 = 2*40 = 4*20 = 5*16 = 8*10 = 10*8 = 16*5 = 20*4 = 40*2 = 80*1 The factor pairs of 80 are (1,80), (2,40), (4,20), (5,16), (8,10), (10,8), (16,5), (20,4), (40,2), (80,1). ### Answer: (1,80), (2,40), (4,20), (5,16), (8,10), (10,8), (16,5), (20,4), (40,2), (80,1)
Expected answer: [(1, 80), (2, 40), (4, 20), (5, 16), (8, 10)]
Correct? No
Problem: Calculate all the factor pairs for the number 96.
InternLM-Math Base 20B:
96 = 2 × 2 × 2 × 2 × 2 × 3 96 = 1 × 96 96 = 2 × 48 96 = 3 × 32 96 = 4 × 24 96 = 6 × 16 96 = 8 × 12 96 = 12 × 8 96 = 16 × 6 96 = 24 × 4 96 = 32 × 3 96 = 48 × 2 96 = 96 × 1
Expected answer: [(1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12)]
Correct? Yes
Problem: Calculate all factor pairs of 19.
InternLM-Math Base 20B:
Reasoning: 19 is a prime number. Therefore, the only factor pair of 19 is 1 and 19. ### Answer: 1 and 19
Expected answer: [(1, 19)]
Correct? Yes
Problem: What are all factor pairs of 37?
InternLM-Math Base 20B:
Reasoning: 37 is a prime number, so it has only two factor pairs: 1 and 37, and 37 and 1. ### Answer: 1 and 37, 37 and 1
Expected answer: [(1, 37)]
Correct? Yes
Problem: Write down all factor pairs of the number 6.
InternLM-Math Base 20B:
Reasoning: 6 = 1 x 6 = 2 x 3 The factor pairs of 6 are (1, 6) and (2, 3). ### Answer: (1, 6) and (2, 3)
Expected answer: [(1, 6), (2, 3)]
Correct? Yes
Problem: List down all the factor pairs of 58.
InternLM-Math Base 20B:
Reasoning: 58 = 1 x 58, 2 x 29, 58 x 1, 29 x 2 ### Answer: 1 x 58, 2 x 29, 58 x 1, 29 x 2
Expected answer: [(1, 58), (2, 29)]
Correct? Yes
Problem: List all the factor pairs of the number 81.
InternLM-Math Base 20B:
Reasoning: 81 = 1 x 81 = 3 x 27 = 9 x 9 The factor pairs of 81 are (1, 81), (3, 27), and (9, 9). ### Answer: (1, 81), (3, 27), and (9, 9)
Expected answer: [(1, 81), (3, 27), (9, 9)]
Correct? Yes
Problem: Please list all factor pairs of the number 85.
InternLM-Math Base 20B:
Reasoning: 85 = 1 x 85, 5 x 17 ### Answer: 1 x 85, 5 x 17
Expected answer: [(1, 85), (5, 17)]
Correct? Yes
Problem: Write down all factor pairs for the number 93.
InternLM-Math Base 20B:
Reasoning: 93 = 1 x 93, 3 x 31, 1 x 93, 3 x 31. ### Answer: 1 x 93, 3 x 31
Expected answer: [(1, 93), (3, 31)]
Correct? Yes
Problem: Identify all factor pairs of 24.
InternLM-Math Base 20B:
1×24, 2×12, 3×8, 4×6, 6×4, 8×3, 12×2, 24×1
Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]
Correct? Yes
Problem: List all the factor pairs of 97.
InternLM-Math Base 20B:
Reasoning: 97 is a prime number, so it has only one factor pair, 1 and 97. ### Answer: 1 and 97
Expected answer: [(1, 97)]
Correct? Yes
Problem: Identify all factor pairs of the number 57.
InternLM-Math Base 20B:
Reasoning: 57 = 3 × 19. The factor pairs of 57 are (1, 57), (3, 19), (57, 1), and (19, 3). ### Answer: (1, 57), (3, 19), (57, 1), and (19, 3)
Expected answer: [(1, 57), (3, 19)]
Correct? Yes
Problem: List down all the factor pairs of 19.
InternLM-Math Base 20B:
Reasoning: 19 is a prime number. It has only one factor pair, which is 1 and 19. ### Answer: 1 and 19
Expected answer: [(1, 19)]
Correct? Yes
Problem: What are all factor pairs of 38?
InternLM-Math Base 20B:
Reasoning: 38 = 2 × 19. The factor pairs of 38 are (1, 38), (2, 19), and (38, 1). ### Answer: (1, 38), (2, 19), (38, 1)
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: Find all the factor pairs of the number 6.
InternLM-Math Base 20B:
Reasoning: 6 = 1 x 6 = 2 x 3 The factor pairs of 6 are (1, 6) and (2, 3). ### Answer: (1, 6) and (2, 3)
Expected answer: [(1, 6), (2, 3)]
Correct? Yes
Problem: Write down all factor pairs of 17.
InternLM-Math Base 20B:
Reasoning: 17 is a prime number. It has only two factors: 1 and 17. ### Answer: 1 and 17
Expected answer: [(1, 17)]
Correct? Yes
Problem: List all factor pairs of 45.
InternLM-Math Base 20B:
Reasoning: 45 = 1 x 45, 3 x 15, 5 x 9, 9 x 5, 15 x 3, 45 x 1. ### Answer: 1 x 45, 3 x 15, 5 x 9, 9 x 5, 15 x 3, 45 x 1
Expected answer: [(1, 45), (3, 15), (5, 9)]
Correct? Yes
Problem: Write down all factor pairs of 36.
InternLM-Math Base 20B:
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?
InternLM-Math Base 20B:
Reasoning: 89 is a prime number, so it has only two factor pairs: 1 and 89, and 89 and 1. ### Answer: 1 and 89, 89 and 1
Expected answer: [(1, 89)]
Correct? Yes
Problem: List all the factor pairs of 89.
InternLM-Math Base 20B:
Reasoning: 89 is a prime number. It has only one factor pair, 1 and 89. ### Answer: 1 and 89
Expected answer: [(1, 89)]
Correct? Yes
Problem: List all the factor pairs of the number 44.
InternLM-Math Base 20B:
Reasoning: 44 = 2 × 2 × 11 The factor pairs of 44 are (1, 44), (2, 22), (4, 11), and (44, 1). ### Answer: (1, 44), (2, 22), (4, 11), (44, 1)
Expected answer: [(1, 44), (2, 22), (4, 11)]
Correct? Yes
Problem: Identify all factor pairs of the number 36.
InternLM-Math Base 20B:
Reasoning: 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6. ### Answer: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 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.
InternLM-Math Base 20B:
Reasoning: 35 = 1 x 35 = 5 x 7 ### Answer: 1 x 35, 5 x 7
Expected answer: [(1, 35), (5, 7)]
Correct? Yes
Problem: Write down all factor pairs of 22.
InternLM-Math Base 20B:
Reasoning: 22 = 1*22 = 2*11 ### Answer: 1*22, 2*11
Expected answer: [(1, 22), (2, 11)]
Correct? Yes
Problem: Find all the factor pairs of 40.
InternLM-Math Base 20B:
Reasoning: 40 = 2 × 2 × 2 × 5 The factor pairs of 40 are (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), and (40, 1). ### Answer: (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), (40, 1)
Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]
Correct? Yes
Problem: List all the factor pairs of the number 64.
InternLM-Math Base 20B:
Reasoning: 64 = 1 x 64, 2 x 32, 4 x 16, 8 x 8. ### Answer: 1 x 64, 2 x 32, 4 x 16, 8 x 8
Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]
Correct? Yes
Problem: Determine all factor pairs of 30.
InternLM-Math Base 20B:
Reasoning: 30 = 2 × 3 × 5. The factor pairs of 30 are (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.
InternLM-Math Base 20B:
Reasoning: 59 is a prime number. Therefore, the only factor pair of 59 is 1 and 59. ### Answer: 1 and 59
Expected answer: [(1, 59)]
Correct? Yes
Problem: List all factor pairs of 18.
InternLM-Math Base 20B:
Reasoning: 18 = 1 x 18, 2 x 9, 3 x 6. ### Answer: 1 x 18, 2 x 9, 3 x 6
Expected answer: [(1, 18), (2, 9), (3, 6)]
Correct? Yes
Problem: Please list all the factor pairs of 61.
InternLM-Math Base 20B:
Reasoning: 61 is a prime number, so it has only one factor pair, 1 and 61. ### Answer: 1 and 61
Expected answer: [(1, 61)]
Correct? Yes
Problem: What are all of the factor pairs of 86?
InternLM-Math Base 20B:
Reasoning: 86 = 2 × 43 = 1 × 86 The factor pairs of 86 are (2, 43) and (1, 86). ### Answer: (2, 43) and (1, 86)
Expected answer: [(1, 86), (2, 43)]
Correct? Yes
Problem: List out all factor pairs of 57.
InternLM-Math Base 20B:
Reasoning: 57 = 1 x 57, 3 x 19 ### Answer: 1 x 57, 3 x 19
Expected answer: [(1, 57), (3, 19)]
Correct? Yes
Problem: What are all factor pairs of 38?
InternLM-Math Base 20B:
Reasoning: 38 = 2 × 19, so the factor pairs of 38 are (1, 38) and (2, 19). ### Answer: (1, 38) and (2, 19)
Expected answer: [(1, 38), (2, 19)]
Correct? Yes
Problem: Please list all factor pairs of 27.
InternLM-Math Base 20B:
Reasoning: 27 = 3*9 = 1*27 The factor pairs of 27 are (1,27) and (3,9).
Expected answer: [(1, 27), (3, 9)]
Correct? No
Problem: List all the factor pairs of the number 78.
InternLM-Math Base 20B:
Reasoning: 78 = 2 x 3 x 13. The factor pairs of 78 are (1, 78), (2, 39), (3, 26), (6, 13), (13, 6), (26, 3), (39, 2), and (78, 1). ### Answer: (1, 78), (2, 39), (3, 26), (6, 13), (13, 6), (26, 3), (39, 2), (78, 1)
Expected answer: [(1, 78), (2, 39), (3, 26), (6, 13)]
Correct? Yes
Problem: List out all the factor pairs of 23.
InternLM-Math Base 20B:
Reasoning: 23 is a prime number, so it has only one factor pair. 23 = 1 x 23 ### Answer: 1 x 23
Expected answer: [(1, 23)]
Correct? Yes
Problem: List down all the factor pairs of 2.
InternLM-Math Base 20B:
2 = 1 x 2 ### Answer: 1 x 2
Expected answer: [(1, 2)]
Correct? Yes
Problem: Write down all the factor pairs of 49.
InternLM-Math Base 20B:
Reasoning: 49 = 1 x 49 = 7 x 7 ### Answer: 1 x 49, 7 x 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.
InternLM-Math Base 20B:
Reasoning: 93 = 3 × 31 93 = 1 × 93 93 = 93 × 1 ### Answer: 3 × 31, 1 × 93, 93 × 1
Expected answer: [(1, 93), (3, 31)]
Correct? Yes