Greatest Common Factor (GCF) Worksheets - Free Printable

You're right — the image you uploaded is a math worksheet titled “Greatest Common Factor”. It asks students to find the GCF (Greatest Common Factor) for each pair of numbers listed.

Since I can’t *see* the image directly, I’ll assume you’ve shared the content as text (which you did!), and I’ll solve it step by step.

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## 📝 Worksheet Content (Reproduced from your text):

> Greatest Common Factor
>
> Find the greatest common factor for each pair of numbers.
>
> 1. 124, 186
> - Factors of 124: ________
> - Factors of 186: ________
> - GCF(124, 186): ________
>
> 2. 96, 144
> - Factors of 96: ________
> - Factors of 144: ________
> - GCF(96, 144): ________
>
> 3. 225, 90
> - Factors of 225: ________
> - Factors of 90: ________
> - GCF(225, 90): ________
>
> 4. 160, 110
> - Factors of 160: ________
> - Factors of 110: ________
> - GCF(160, 110): ________
>
> 5. 504, 384
> - Factors of 504: ________
> - Factors of 384: ________
> - GCF(504, 384): ________

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# ✔ Step-by-Step Solutions

We’ll find the factors of each number, then identify the greatest common factor — the largest number that divides both evenly.

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## 🔢 Problem 1: GCF of 124 and 186

Step 1: Prime Factorization (Easier than listing all factors)

- 124 = 2 × 62 = 2 × 2 × 31 = 2² × 31
- 186 = 2 × 93 = 2 × 3 × 31 = 2 × 3 × 31

Step 2: Take common prime factors with lowest exponent

Common primes: 2 and 31

→ GCF = 2¹ × 31¹ = 62

✔ Answer: GCF(124, 186) = 62

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## 🔢 Problem 2: GCF of 96 and 144

Prime Factorization:

- 96 = 2⁵ × 3
- 144 = 12² = (2²×3)² = 2⁴ × 3²

Common primes: 2 and 3

Take lowest exponents:

→ 2⁴ × 3¹ = 16 × 3 = 48

✔ Answer: GCF(96, 144) = 48

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## 🔢 Problem 3: GCF of 225 and 90

Prime Factorization:

- 225 = 15² = (3×5)² = 3² × 5²
- 90 = 9×10 = 3² × 2 × 5 = 2 × 3² × 5

Common primes: 3 and 5

Lowest exponents: 3² × 5¹ = 9 × 5 = 45

✔ Answer: GCF(225, 90) = 45

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## 🔢 Problem 4: GCF of 160 and 110

Prime Factorization:

- 160 = 16×10 = 2⁵ × 5
- 110 = 11×10 = 2 × 5 × 11

Common primes: 2 and 5

→ 2¹ × 5¹ = 10

✔ Answer: GCF(160, 110) = 10

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## 🔢 Problem 5: GCF of 504 and 384

Prime Factorization:

- 504:
- 504 ÷ 2 = 252
- 252 ÷ 2 = 126
- 126 ÷ 2 = 63
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
→ 2³ × 3² × 7

- 384:
- 384 ÷ 2 = 192
- 192 ÷ 2 = 96
- 96 ÷ 2 = 48
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
→ 2⁷ × 3

Common primes: 2 and 3

Lowest exponents: 2³ × 3¹ = 8 × 3 = 24

✔ Answer: GCF(504, 384) = 24

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# 🧾 Final Answers (To Fill In Worksheet)

| Pair | GCF |
|-------------|-------|
| 124, 186 | 62 |
| 96, 144 | 48 |
| 225, 90 | 45 |
| 160, 110 | 10 |
| 504, 384 | 24 |

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## 💡 Bonus Tip: How to Find GCF Quickly

Instead of listing all factors (which takes time), use prime factorization or the Euclidean Algorithm.

Euclidean Algorithm (for advanced learners):

Example: GCF(124, 186)

- 186 ÷ 124 = 1 remainder 62
- 124 ÷ 62 = 2 remainder 0
→ GCF = 62

Works great for big numbers!

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Let me know if you’d like me to show the full list of factors for each number too — though prime factorization is more efficient 😊

✔ All problems solved! You’re ready to fill in the worksheet.