Greatest Common Factor Worksheet page - Free Printable

You’ve uploaded a worksheet titled “GREATEST COMMON FACTOR SHEET 5A ANSWERS”, which shows the solutions to four problems asking for the Greatest Common Factor (GCF) of three numbers each. The GCF is the largest number that divides all given numbers without a remainder.

Let’s go through each problem step by step and explain how the answers were found.

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🔹 Problem 1: Find the GCF of 20, 15, and 12.

Step 1: List all factors of each number.

- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 15: 1, 3, 5, 15
- Factors of 12: 1, 2, 3, 4, 6, 12

Step 2: Find common factors.
Look for numbers that appear in ALL THREE lists.

→ Only 1 appears in all three lists.

✔ So, GCF(20, 15, 12) = 1

*(Note: Since there’s no larger common factor, these numbers are “relatively prime” as a set.)*

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🔹 Problem 2: Find the GCF of 21, 35, and 28.

Step 1: List factors.

- Factors of 21: 1, 3, 7, 21
- Factors of 35: 1, 5, 7, 35
- Factors of 28: 1, 2, 4, 7, 14, 28

Step 2: Find common factors.

→ Common factors: 1 and 7

Step 3: Pick the greatest.

✔ So, GCF(21, 35, 28) = 7

*(This makes sense — 7 divides all three: 21÷7=3, 35÷7=5, 28÷7=4.)*

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🔹 Problem 3: Find the GCF of 24, 18, and 30.

Step 1: List factors.

- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Step 2: Find common factors.

→ Common factors: 1, 2, 3, 6

Step 3: Pick the greatest.

✔ So, GCF(24, 18, 30) = 6

*(Check: 24÷6=4, 18÷6=3, 30÷6=5 — all whole numbers.)*

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🔹 Problem 4: Find the GCF of 40, 28, and 18.

Step 1: List factors.

- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 18: 1, 2, 3, 6, 9, 18

Step 2: Find common factors.

→ Common factors: 1, 2

Step 3: Pick the greatest.

✔ So, GCF(40, 28, 18) = 2

*(Check: 40÷2=20, 28÷2=14, 18÷2=9 — all divisible.)*

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## ✔ Final Answers Summary:

1. GCF(20, 15, 12) = 1
2. GCF(21, 35, 28) = 7
3. GCF(24, 18, 30) = 6
4. GCF(40, 28, 18) = 2

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## 💡 Tip: Alternative Method (Prime Factorization)

You can also find GCF using prime factorization:

Example: GCF(24, 18, 30)

- 24 = 2³ × 3
- 18 = 2 × 3²
- 30 = 2 × 3 × 5

Take the lowest power of common primes:
→ 2¹ × 3¹ = 6 → Same answer!

This method is faster for larger numbers.

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✔ All answers on your sheet are correct! The explanations above show you *why* they’re correct. Great job practicing GCFs!