Let’s solve each problem step by step. We’ll find all the factors of each number, then pick the biggest one that appears in all lists — that’s the HCF (Highest Common Factor).
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1) 9 and 12
Factors of 9:
1, 3, 9
Factors of 12:
1, 2, 3, 4, 6, 12
Common factors: 1, 3
→ Highest is
3
HCF =
3
---
2) 24 and 28
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Factors of 28:
1, 2, 4, 7, 14, 28
Common factors: 1, 2, 4
→ Highest is
4
HCF =
4
---
3) 63 and 72
Factors of 63:
1, 3, 7, 9, 21, 63
Factors of 72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors: 1, 3, 9
→ Highest is
9
HCF =
9
---
4) 36 and 84
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Common factors: 1, 2, 3, 4, 6, 12
→ Highest is
12
HCF =
12
---
5) 13, 39, 52
Factors of 13:
1, 13 (it’s a prime number)
Factors of 39:
1, 3, 13, 39
Factors of 52:
1, 2, 4, 13, 26, 52
Common factors: 1, 13
→ Highest is
13
HCF =
13
---
6) 30, 45, 60
Factors of 30:
1, 2, 3, 5, 6, 10, 15, 30
Factors of 45:
1, 3, 5, 9, 15, 45
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors: 1, 3, 5, 15
→ Highest is
15
HCF =
15
---
Final Answer:
1)
9: 1, 3, 9
12: 1, 2, 3, 4, 6, 12
HCF: 3
2)
24: 1, 2, 3, 4, 6, 8, 12, 24
28: 1, 2, 4, 7, 14, 28
HCF: 4
3)
63: 1, 3, 7, 9, 21, 63
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
HCF: 9
4)
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
HCF: 12
5)
13: 1, 13
39: 1, 3, 13, 39
52: 1, 2, 4, 13, 26, 52
HCF: 13
6)
30: 1, 2, 3, 5, 6, 10, 15, 30
45: 1, 3, 5, 9, 15, 45
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
HCF: 15
Parent Tip: Review the logic above to help your child master the concept of hcf worksheet.
