Let's solve the
Greatest Common Factor (GCF) problems from the worksheet step by step. The goal is to find the
largest number that divides all three given numbers in each problem.
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We'll go through each problem one by one, using prime factorization or listing factors where necessary.
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1) 56, 42, 98
- Prime factorization:
- 56 = 2 × 2 × 2 × 7 = $2^3 \times 7$
- 42 = 2 × 3 × 7
- 98 = 2 × 7 × 7 = $2 \times 7^2$
- Common factors: 2 and 7 → $2 \times 7 = 14$
✔ GCF = 14
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2) 77, 33, 22
- 77 = 7 × 11
- 33 = 3 × 11
- 22 = 2 × 11
- Only common factor: 11
✔ GCF = 11
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3) 80, 16, 96
- 80 = 2⁴ × 5
- 16 = 2⁴
- 96 = 2⁵ × 3
- All divisible by $2^4 = 16$
✔ GCF = 16
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4) 65, 39, 13
- 65 = 5 × 13
- 39 = 3 × 13
- 13 = 13
- All divisible by 13
✔ GCF = 13
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5) 14, 49, 7
- 14 = 2 × 7
- 49 = 7²
- 7 = 7
- All divisible by 7
✔ GCF = 7
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6) 48, 64, 32
- 48 = 2⁴ × 3
- 64 = 2⁶
- 32 = 2⁵
- Common: $2^4 = 16$
✔ GCF = 16
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7) 16, 72, 80
- 16 = 2⁴
- 72 = 2³ × 3²
- 80 = 2⁴ × 5
- Common: $2^3 = 8$
✔ GCF = 8
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8) 99, 11, 88
- 99 = 3² × 11
- 11 = 11
- 88 = 2³ × 11
- All divisible by 11
✔ GCF = 11
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9) 4, 37, 51
- 4 = 2²
- 37 = prime
- 51 = 3 × 17
- No common factor other than 1
✔ GCF = 1
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10) 7, 28, 98
- 7 = 7
- 28 = 2² × 7
- 98 = 2 × 7²
- All divisible by 7
✔ GCF = 7
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11) 8, 57, 34
- 8 = 2³
- 57 = 3 × 19
- 34 = 2 × 17
- Only common factor: none (except 1)
✔ GCF = 1
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12) 48, 87, 6
- 48 = 2⁴ × 3
- 87 = 3 × 29
- 6 = 2 × 3
- Common factor: 3
✔ GCF = 3
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13) 24, 90, 78
- 24 = 2³ × 3
- 90 = 2 × 3² × 5
- 78 = 2 × 3 × 13
- Common: 2 × 3 = 6
✔ GCF = 6
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14) 64, 48, 16
- 64 = 2⁶
- 48 = 2⁴ × 3
- 16 = 2⁴
- Common: $2^4 = 16$
✔ GCF = 16
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15) 77, 49, 56
- 77 = 7 × 11
- 49 = 7²
- 56 = 2³ × 7
- All divisible by 7
✔ GCF = 7
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16) 22, 77, 66
- 22 = 2 × 11
- 77 = 7 × 11
- 66 = 2 × 3 × 11
- All divisible by 11
✔ GCF = 11
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##
✔ Final Answers:
| Problem | Numbers | GCF |
|--------|---------------------|-----|
| 1 | 56, 42, 98 | 14 |
| 2 | 77, 33, 22 | 11 |
| 3 | 80, 16, 96 | 16 |
| 4 | 65, 39, 13 | 13 |
| 5 | 14, 49, 7 | 7 |
| 6 | 48, 64, 32 | 16 |
| 7 | 16, 72, 80 | 8 |
| 8 | 99, 11, 88 | 11 |
| 9 | 4, 37, 51 | 1 |
| 10 | 7, 28, 98 | 7 |
| 11 | 8, 57, 34 | 1 |
| 12 | 48, 87, 6 | 3 |
| 13 | 24, 90, 78 | 6 |
| 14 | 64, 48, 16 | 16 |
| 15 | 77, 49, 56 | 7 |
| 16 | 22, 77, 66 | 11 |
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🔍 Tips for Finding GCF:
-
Prime factorization: Break down each number into primes.
-
List common prime factors, take the lowest power.
- If no common factor other than 1 → GCF = 1.
This method works best for larger numbers. For smaller ones, you can list all factors.
Let me know if you'd like a printable version or explanation of any specific problem!
Parent Tip: Review the logic above to help your child master the concept of factoring using gcf worksheet pdf.
