Let's solve each problem step by step to find the
Highest Common Factor (HCF), also known as the
Greatest Common Divisor (GCD), of the given pairs of numbers.
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🔹 Method:
We can use either:
-
Prime factorization, or
-
Listing factors (for smaller numbers)
We'll go through each pair and explain.
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1. 6 and 36
Factors of 6: 1, 2, 3, 6
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 6
✔ HCF = 6
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2. 20 and 2
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 2: 1, 2
Common factors: 1, 2
✔ HCF = 2
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3. 2 and 38
Factors of 2: 1, 2
Factors of 38: 1, 2, 19, 38
Common factors: 1, 2
✔ HCF = 2
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4. 33 and 22
Factors of 33: 1, 3, 11, 33
Factors of 22: 1, 2, 11, 22
Common factors: 1, 11
✔ HCF = 11
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5. 20 and 8
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 8: 1, 2, 4, 8
Common factors: 1, 2, 4
✔ HCF = 4
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6. 39 and 3
Factors of 39: 1, 3, 13, 39
Factors of 3: 1, 3
Common factors: 1, 3
✔ HCF = 3
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7. 35 and 5
Factors of 35: 1, 5, 7, 35
Factors of 5: 1, 5
Common factors: 1, 5
✔ HCF = 5
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8. 22 and 50
Factors of 22: 1, 2, 11, 22
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors: 1, 2
✔ HCF = 2
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9. 20 and 35
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 35: 1, 5, 7, 35
Common factors: 1, 5
✔ HCF = 5
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10. 44 and 11
Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 11: 1, 11
Common factors: 1, 11
✔ HCF = 11
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✔ Final Answers:
| Problem | Numbers | HCF |
|--------|-------------|-----|
| 1 | 6, 36 | 6 |
| 2 | 20, 2 | 2 |
| 3 | 2, 38 | 2 |
| 4 | 33, 22 | 11 |
| 5 | 20, 8 | 4 |
| 6 | 39, 3 | 3 |
| 7 | 35, 5 | 5 |
| 8 | 22, 50 | 2 |
| 9 | 20, 35 | 5 |
| 10 | 44, 11 | 11 |
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You can fill in the blanks on your worksheet accordingly!
Let me know if you'd like a visual method (like prime factor trees) for any of them! 😊
Parent Tip: Review the logic above to help your child master the concept of greatest common factors worksheet.
