Let’s solve each problem step by step to find the Greatest Common Factor (GCF) using the long division method — also known as the Euclidean algorithm.
The idea is simple:
- Divide the bigger number by the smaller one.
- Then divide the divisor by the remainder.
- Keep going until the remainder is 0.
- The last non-zero remainder is the GCF.
We’ll go through all 15 problems carefully.
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1. 45, 55
55 ÷ 45 = 1 R10
45 ÷ 10 = 4 R5
10 ÷ 5 = 2 R0 → GCF =
5
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2. 30, 60
60 ÷ 30 = 2 R0 → GCF =
30
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3. 12, 40
40 ÷ 12 = 3 R4
12 ÷ 4 = 3 R0 → GCF =
4
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4. 36, 75
75 ÷ 36 = 2 R3
36 ÷ 3 = 12 R0 → GCF =
3
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5. 44, 58
58 ÷ 44 = 1 R14
44 ÷ 14 = 3 R2
14 ÷ 2 = 7 R0 → GCF =
2
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6. 33, 39
39 ÷ 33 = 1 R6
33 ÷ 6 = 5 R3
6 ÷ 3 = 2 R0 → GCF =
3
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7. 28, 44
44 ÷ 28 = 1 R16
28 ÷ 16 = 1 R12
16 ÷ 12 = 1 R4
12 ÷ 4 = 3 R0 → GCF =
4
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8. 30, 75
75 ÷ 30 = 2 R15
30 ÷ 15 = 2 R0 → GCF =
15
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9. 25, 40
40 ÷ 25 = 1 R15
25 ÷ 15 = 1 R10
15 ÷ 10 = 1 R5
10 ÷ 5 = 2 R0 → GCF =
5
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10. 75, 90
90 ÷ 75 = 1 R15
75 ÷ 15 = 5 R0 → GCF =
15
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11. 60, 75
75 ÷ 60 = 1 R15
60 ÷ 15 = 4 R0 → GCF =
15
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12. 50, 60
60 ÷ 50 = 1 R10
50 ÷ 10 = 5 R0 → GCF =
10
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13. 40, 80
80 ÷ 40 = 2 R0 → GCF =
40
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14. 18, 81
81 ÷ 18 = 4 R9
18 ÷ 9 = 2 R0 → GCF =
9
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15. 60, 90
90 ÷ 60 = 1 R30
60 ÷ 30 = 2 R0 → GCF =
30
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Final Answer:
1. 5
2. 30
3. 4
4. 3
5. 2
6. 3
7. 4
8. 15
9. 5
10. 15
11. 15
12. 10
13. 40
14. 9
15. 30
Parent Tip: Review the logic above to help your child master the concept of math greatest common factor worksheet.
