Let's solve the worksheet step by step. The task is to
find the Highest Common Factor (HCF) of pairs of numbers by listing their factors and identifying the largest common factor.
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🔷 What is HCF?
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'll find:
1. All
factors of each number.
2. The
common factors.
3. The
highest among them → that’s the HCF.
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Let’s go through each problem:
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1. 24, 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
✔ Answer: 8
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2. 8, 36
-
Factors of 8:
1, 2, 4, 8
-
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
-
Common factors: 1, 2, 4
-
HCF = 4
✔ Answer: 4
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3. 14, 19
-
Factors of 14:
1, 2, 7, 14
-
Factors of 19:
1, 19 (19 is prime)
-
Common factors: 1
-
HCF = 1
✔ Answer: 1
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4. 10, 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
-
HCF = 10
✔ Answer: 10
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5. 5, 7
-
Factors of 5:
1, 5
-
Factors of 7:
1, 7
-
Common factors: 1
-
HCF = 1
✔ Answer: 1
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6. 28, 35
-
Factors of 28:
1, 2, 4, 7, 14, 28
-
Factors of 35:
1, 5, 7, 35
-
Common factors: 1, 7
-
HCF = 7
✔ Answer: 7
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7. 31, 21
-
Factors of 31:
1, 31 (31 is prime)
-
Factors of 21:
1, 3, 7, 21
-
Common factors: 1
-
HCF = 1
✔ Answer: 1
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8. 42, 60
-
Factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
-
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
-
Common factors: 1, 2, 3, 6
-
HCF = 6
✔ Answer: 6
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9. 81, 36
-
Factors of 81:
1, 3, 9, 27, 81
-
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
-
Common factors: 1, 3, 9
-
HCF = 9
✔ Answer: 9
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10. 30, 63
-
Factors of 30:
1, 2, 3, 5, 6, 10, 15, 30
-
Factors of 63:
1, 3, 7, 9, 21, 63
-
Common factors: 1, 3
-
HCF = 3
✔ Answer: 3
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✔ Final Answers:
| Problem | Numbers | HCF |
|--------|--------|-----|
| 1 | 24, 32 |
8 |
| 2 | 8, 36 |
4 |
| 3 | 14, 19 |
1 |
| 4 | 10, 30 |
10 |
| 5 | 5, 7 |
1 |
| 6 | 28, 35 |
7 |
| 7 | 31, 21 |
1 |
| 8 | 42, 60 |
6 |
| 9 | 81, 36 |
9 |
| 10 | 30, 63 |
3 |
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📝 Summary Tips:
- Always list all factors carefully.
- Look for common ones.
- Pick the
largest common factor.
- If numbers are
prime, their HCF is usually
1 unless they're the same number.
Let me know if you'd like a printable version or want to learn the
prime factorization method for finding HCF faster!
Parent Tip: Review the logic above to help your child master the concept of factors worksheet grade 4.
