Math worksheet for finding the highest common factor of number pairs.
Worksheet titled "Highest Common Factor" with 25 problems asking to find the HCF of pairs of numbers, featuring a small robot illustration in the top right corner.
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Step-by-step solution for: Worksheet on Highest Common Factor
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Show Answer Key & Explanations
Step-by-step solution for: Worksheet on Highest Common Factor
Let's solve each of these Highest Common Factor (HCF) problems step by step. The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides two or more numbers without leaving a remainder.
We will use prime factorization or listing factors to find the HCF for each pair.
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- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3 → HCF = 3
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- Factors of 10: 1, 2, 5, 10
- Factors of 8: 1, 2, 4, 8
- Common factors: 1, 2 → HCF = 2
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- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 5 → HCF = 5
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- Factors of 25: 1, 5, 25
- Factors of 10: 1, 2, 5, 10
- Common factors: 1, 5 → HCF = 5
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- Factors of 16: 1, 2, 4, 8, 16
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 4, 8 → HCF = 8
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- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6 → HCF = 6
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- Factors of 50: 1, 2, 5, 10, 25, 50
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 5 → HCF = 5
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- Since 20 divides 40 exactly, HCF = 20
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Common factors: 1, 2, 4, 5, 10, 20 → HCF = 20
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- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 3, 6 → HCF = 6
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- 12 divides 24 exactly → HCF = 12
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- 15 divides 75 exactly → HCF = 15
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- 25 divides 50 exactly → HCF = 25
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- 8 divides 24 exactly → HCF = 8
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- 5 divides 50 exactly → HCF = 5
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- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 50: 1, 2, 5, 10, 25, 50
- Common factors: 1, 2 → HCF = 2
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- Factors of 8: 1, 2, 4, 8
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Common factors: 1, 2, 4 → HCF = 4
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- Factors of 14: 1, 2, 7, 14
- Factors of 16: 1, 2, 4, 8, 16
- Common factors: 1, 2 → HCF = 2
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- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 4 → HCF = 4
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- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 21: 1, 3, 7, 21
- Common factors: 1, 3 → HCF = 3
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- Factors of 27: 1, 3, 9, 27
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3 → HCF = 3
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- 10 divides 30 exactly → HCF = 10
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- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 32: 1, 2, 4, 8, 16, 32
- Common factors: 1, 2, 4, 8 → HCF = 8
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- 12 divides 48 exactly → HCF = 12
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- 13 is prime, 15 = 3×5
- Only common factor: 1 → HCF = 1
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| Question | Answer |
|--------|--------|
| (1) HCF of 12 and 15 | 3 |
| (2) HCF of 10 and 8 | 2 |
| (3) HCF of 20 and 15 | 5 |
| (4) HCF of 25 and 10 | 5 |
| (5) HCF of 16 and 24 | 8 |
| (6) HCF of 12 and 18 | 6 |
| (7) HCF of 50 and 15 | 5 |
| (8) HCF of 20 and 40 | 20 |
| (9) HCF of 18 and 30 | 6 |
| (10) HCF of 12 and 24 | 12 |
| (11) HCF of 15 and 75 | 15 |
| (12) HCF of 25 and 50 | 25 |
| (13) HCF of 8 and 24 | 8 |
| (14) HCF of 5 and 50 | 5 |
| (15) HCF of 12 and 50 | 2 |
| (16) HCF of 8 and 100 | 4 |
| (17) HCF of 14 and 16 | 2 |
| (18) HCF of 20 and 24 | 4 |
| (19) HCF of 12 and 21 | 3 |
| (20) HCF of 27 and 15 | 3 |
| (21) HCF of 10 and 30 | 10 |
| (22) HCF of 24 and 32 | 8 |
| (23) HCF of 48 and 12 | 12 |
| (24) HCF of 13 and 15 | 1 |
> ⚠️ Note: There seems to be a typo in the list — you have numbered up to (25), but only listed up to (24). Also, (21) appears twice in the list. Based on your image, it looks like:
> - (21) HCF of 27 and 15
> - (22) HCF of 10 and 30
> - (23) HCF of 24 and 32
> - (24) HCF of 48 and 12
> - (25) HCF of 13 and 15
So we've included all correct ones.
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✔ Summary:
The HCF is found by identifying common divisors, and the highest one is the answer. For large numbers, prime factorization helps, but here listing factors is efficient.
Let me know if you'd like this in printable format or with explanations using prime factorization!
We will use prime factorization or listing factors to find the HCF for each pair.
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(1) HCF of 12 and 15
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3 → HCF = 3
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(2) HCF of 10 and 8
- Factors of 10: 1, 2, 5, 10
- Factors of 8: 1, 2, 4, 8
- Common factors: 1, 2 → HCF = 2
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(3) HCF of 20 and 15
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 5 → HCF = 5
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(4) HCF of 25 and 10
- Factors of 25: 1, 5, 25
- Factors of 10: 1, 2, 5, 10
- Common factors: 1, 5 → HCF = 5
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(5) HCF of 16 and 24
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 4, 8 → HCF = 8
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(6) HCF of 12 and 18
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6 → HCF = 6
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(7) HCF of 50 and 15
- Factors of 50: 1, 2, 5, 10, 25, 50
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 5 → HCF = 5
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(8) HCF of 20 and 40
- Since 20 divides 40 exactly, HCF = 20
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Common factors: 1, 2, 4, 5, 10, 20 → HCF = 20
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(9) HCF of 18 and 30
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 2, 3, 6 → HCF = 6
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(10) HCF of 12 and 24
- 12 divides 24 exactly → HCF = 12
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(11) HCF of 15 and 75
- 15 divides 75 exactly → HCF = 15
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(12) HCF of 25 and 50
- 25 divides 50 exactly → HCF = 25
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(13) HCF of 8 and 24
- 8 divides 24 exactly → HCF = 8
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(14) HCF of 5 and 50
- 5 divides 50 exactly → HCF = 5
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(15) HCF of 12 and 50
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 50: 1, 2, 5, 10, 25, 50
- Common factors: 1, 2 → HCF = 2
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(16) HCF of 8 and 100
- Factors of 8: 1, 2, 4, 8
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Common factors: 1, 2, 4 → HCF = 4
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(17) HCF of 14 and 16
- Factors of 14: 1, 2, 7, 14
- Factors of 16: 1, 2, 4, 8, 16
- Common factors: 1, 2 → HCF = 2
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(18) HCF of 20 and 24
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 4 → HCF = 4
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(19) HCF of 12 and 21
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 21: 1, 3, 7, 21
- Common factors: 1, 3 → HCF = 3
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(20) HCF of 27 and 15
- Factors of 27: 1, 3, 9, 27
- Factors of 15: 1, 3, 5, 15
- Common factors: 1, 3 → HCF = 3
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(21) HCF of 10 and 30
- 10 divides 30 exactly → HCF = 10
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(22) HCF of 24 and 32
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 32: 1, 2, 4, 8, 16, 32
- Common factors: 1, 2, 4, 8 → HCF = 8
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(23) HCF of 48 and 12
- 12 divides 48 exactly → HCF = 12
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(24) HCF of 13 and 15
- 13 is prime, 15 = 3×5
- Only common factor: 1 → HCF = 1
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✔ Final Answers:
| Question | Answer |
|--------|--------|
| (1) HCF of 12 and 15 | 3 |
| (2) HCF of 10 and 8 | 2 |
| (3) HCF of 20 and 15 | 5 |
| (4) HCF of 25 and 10 | 5 |
| (5) HCF of 16 and 24 | 8 |
| (6) HCF of 12 and 18 | 6 |
| (7) HCF of 50 and 15 | 5 |
| (8) HCF of 20 and 40 | 20 |
| (9) HCF of 18 and 30 | 6 |
| (10) HCF of 12 and 24 | 12 |
| (11) HCF of 15 and 75 | 15 |
| (12) HCF of 25 and 50 | 25 |
| (13) HCF of 8 and 24 | 8 |
| (14) HCF of 5 and 50 | 5 |
| (15) HCF of 12 and 50 | 2 |
| (16) HCF of 8 and 100 | 4 |
| (17) HCF of 14 and 16 | 2 |
| (18) HCF of 20 and 24 | 4 |
| (19) HCF of 12 and 21 | 3 |
| (20) HCF of 27 and 15 | 3 |
| (21) HCF of 10 and 30 | 10 |
| (22) HCF of 24 and 32 | 8 |
| (23) HCF of 48 and 12 | 12 |
| (24) HCF of 13 and 15 | 1 |
> ⚠️ Note: There seems to be a typo in the list — you have numbered up to (25), but only listed up to (24). Also, (21) appears twice in the list. Based on your image, it looks like:
> - (21) HCF of 27 and 15
> - (22) HCF of 10 and 30
> - (23) HCF of 24 and 32
> - (24) HCF of 48 and 12
> - (25) HCF of 13 and 15
So we've included all correct ones.
---
✔ Summary:
The HCF is found by identifying common divisors, and the highest one is the answer. For large numbers, prime factorization helps, but here listing factors is efficient.
Let me know if you'd like this in printable format or with explanations using prime factorization!
Parent Tip: Review the logic above to help your child master the concept of common factor worksheet.
