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 problem step by step. We’re looking for the Highest Common Factor (HCF) — that means the biggest number that divides both numbers evenly (with no remainder).
We’ll go one by one:
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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 → Highest is 3
✔ Answer: 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 → Highest is 2
✔ Answer: 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 → Highest is 5
✔ Answer: 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 → Highest is 5
✔ Answer: 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 → Highest is 8
✔ Answer: 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 → Highest is 6
✔ Answer: 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 → Highest is 5
✔ Answer: 5
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(8) HCF of 20 and 40
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 → Highest is 20
✔ Answer: 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 → Highest is 6
✔ Answer: 6
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(10) HCF of 12 and 24
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 4, 6, 12 → Highest is 12
✔ Answer: 12
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(11) HCF of 15 and 75
Factors of 15: 1, 3, 5, 15
Factors of 75: 1, 3, 5, 15, 25, 75
Common factors: 1, 3, 5, 15 → Highest is 15
✔ Answer: 15
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(12) HCF of 25 and 50
Factors of 25: 1, 5, 25
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors: 1, 5, 25 → Highest is 25
✔ Answer: 25
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(13) HCF of 8 and 24
Factors of 8: 1, 2, 4, 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4, 8 → Highest is 8
✔ Answer: 8
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(14) HCF of 5 and 50
Factors of 5: 1, 5
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors: 1, 5 → Highest is 5
✔ Answer: 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 → Highest is 2
✔ Answer: 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 → Highest is 4
✔ Answer: 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 → Highest is 2
✔ Answer: 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 → Highest is 4
✔ Answer: 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 → Highest is 3
✔ Answer: 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 → Highest is 3
✔ Answer: 3
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(21) HCF of 10 and 30
Factors of 10: 1, 2, 5, 10
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 5, 10 → Highest is 10
✔ Answer: 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 → Highest is 8
✔ Answer: 8
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(23) HCF of 48 and 12
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 3, 4, 6, 12 → Highest is 12
✔ Answer: 12
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(24) HCF of 13 and 15
Factors of 13: 1, 13 (it’s a prime number!)
Factors of 15: 1, 3, 5, 15
Only common factor: 1
✔ Answer: 1
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Final Answer:
(1) 3
(2) 2
(3) 5
(4) 5
(5) 8
(6) 6
(7) 5
(8) 20
(9) 6
(10) 12
(11) 15
(12) 25
(13) 8
(14) 5
(15) 2
(16) 4
(17) 2
(18) 4
(19) 3
(20) 3
(21) 10
(22) 8
(23) 12
(24) 1
We’ll go one by one:
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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 → Highest is 3
✔ Answer: 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 → Highest is 2
✔ Answer: 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 → Highest is 5
✔ Answer: 5
---
(4) HCF of 25 and 10
Factors of 25: 1, 5, 25
Factors of 10: 1, 2, 5, 10
Common factors: 1, 5 → Highest is 5
✔ Answer: 5
---
(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 → Highest is 8
✔ Answer: 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 → Highest is 6
✔ Answer: 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 → Highest is 5
✔ Answer: 5
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(8) HCF of 20 and 40
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 → Highest is 20
✔ Answer: 20
---
(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 → Highest is 6
✔ Answer: 6
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(10) HCF of 12 and 24
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 4, 6, 12 → Highest is 12
✔ Answer: 12
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(11) HCF of 15 and 75
Factors of 15: 1, 3, 5, 15
Factors of 75: 1, 3, 5, 15, 25, 75
Common factors: 1, 3, 5, 15 → Highest is 15
✔ Answer: 15
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(12) HCF of 25 and 50
Factors of 25: 1, 5, 25
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors: 1, 5, 25 → Highest is 25
✔ Answer: 25
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(13) HCF of 8 and 24
Factors of 8: 1, 2, 4, 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4, 8 → Highest is 8
✔ Answer: 8
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(14) HCF of 5 and 50
Factors of 5: 1, 5
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors: 1, 5 → Highest is 5
✔ Answer: 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 → Highest is 2
✔ Answer: 2
---
(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 → Highest is 4
✔ Answer: 4
---
(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 → Highest is 2
✔ Answer: 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 → Highest is 4
✔ Answer: 4
---
(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 → Highest is 3
✔ Answer: 3
---
(20) HCF of 27 and 15
Factors of 27: 1, 3, 9, 27
Factors of 15: 1, 3, 5, 15
Common factors: 1, 3 → Highest is 3
✔ Answer: 3
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(21) HCF of 10 and 30
Factors of 10: 1, 2, 5, 10
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 5, 10 → Highest is 10
✔ Answer: 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 → Highest is 8
✔ Answer: 8
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(23) HCF of 48 and 12
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 3, 4, 6, 12 → Highest is 12
✔ Answer: 12
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(24) HCF of 13 and 15
Factors of 13: 1, 13 (it’s a prime number!)
Factors of 15: 1, 3, 5, 15
Only common factor: 1
✔ Answer: 1
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Final Answer:
(1) 3
(2) 2
(3) 5
(4) 5
(5) 8
(6) 6
(7) 5
(8) 20
(9) 6
(10) 12
(11) 15
(12) 25
(13) 8
(14) 5
(15) 2
(16) 4
(17) 2
(18) 4
(19) 3
(20) 3
(21) 10
(22) 8
(23) 12
(24) 1
Parent Tip: Review the logic above to help your child master the concept of hcf worksheet.
