Grade 6 Factoring Worksheet: Find the Greatest Common Factor (GCF) of three numbers.
Grade 6 worksheet on finding the greatest common factor (GCF) of three numbers, featuring 12 problems with number pairs for practice.
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Step-by-step solution for: Grade 6 Factoring Worksheets: Greatest common factor of 3 numbers ...
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Show Answer Key & Explanations
Step-by-step solution for: Grade 6 Factoring Worksheets: Greatest common factor of 3 numbers ...
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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- 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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- 77 = 7 × 11
- 33 = 3 × 11
- 22 = 2 × 11
- Only common factor: 11
✔ GCF = 11
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- 80 = 2⁴ × 5
- 16 = 2⁴
- 96 = 2⁵ × 3
- All divisible by $2^4 = 16$
✔ GCF = 16
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- 65 = 5 × 13
- 39 = 3 × 13
- 13 = 13
- All divisible by 13
✔ GCF = 13
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- 14 = 2 × 7
- 49 = 7²
- 7 = 7
- All divisible by 7
✔ GCF = 7
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- 48 = 2⁴ × 3
- 64 = 2⁶
- 32 = 2⁵
- Common: $2^4 = 16$
✔ GCF = 16
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- 16 = 2⁴
- 72 = 2³ × 3²
- 80 = 2⁴ × 5
- Common: $2^3 = 8$
✔ GCF = 8
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- 99 = 3² × 11
- 11 = 11
- 88 = 2³ × 11
- All divisible by 11
✔ GCF = 11
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- 4 = 2²
- 37 = prime
- 51 = 3 × 17
- No common factor other than 1
✔ GCF = 1
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- 7 = 7
- 28 = 2² × 7
- 98 = 2 × 7²
- All divisible by 7
✔ GCF = 7
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- 8 = 2³
- 57 = 3 × 19
- 34 = 2 × 17
- Only common factor: none except 1
✔ GCF = 1
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- 48 = 2⁴ × 3
- 87 = 3 × 29
- 6 = 2 × 3
- Common: 3
✔ GCF = 3
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- 24 = 2³ × 3
- 90 = 2 × 3² × 5
- 78 = 2 × 3 × 13
- Common: 2 × 3 = 6
✔ GCF = 6
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- 64 = 2⁶
- 48 = 2⁴ × 3
- 16 = 2⁴
- Common: $2^4 = 16$
✔ GCF = 16
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- 77 = 7 × 11
- 49 = 7²
- 56 = 2³ × 7
- All divisible by 7
✔ GCF = 7
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- 22 = 2 × 11
- 77 = 7 × 11
- 66 = 2 × 3 × 11
- All divisible by 11
✔ GCF = 11
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| 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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To find the GCF of three numbers, you can:
1. Prime factorize each number.
2. Identify common prime factors.
3. Multiply the lowest powers of shared primes.
Alternatively, use the Euclidean algorithm for two numbers at a time.
For example:
GCF(56, 42, 98) →
First, GCF(56, 42) = 14
Then, GCF(14, 98) = 14 → final answer.
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Let me know if you'd like this as a printable PDF or need help with any specific method!
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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: 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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🔍 How to Find GCF:
To find the GCF of three numbers, you can:
1. Prime factorize each number.
2. Identify common prime factors.
3. Multiply the lowest powers of shared primes.
Alternatively, use the Euclidean algorithm for two numbers at a time.
For example:
GCF(56, 42, 98) →
First, GCF(56, 42) = 14
Then, GCF(14, 98) = 14 → final answer.
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Let me know if you'd like this as a printable PDF or need help with any specific method!
Parent Tip: Review the logic above to help your child master the concept of hcf worksheet.
