What is the GCF of the two numbers below $$ 32 \quad 20 $$

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UpStudy AI · Accepted Answer

To find the **Greatest Common Factor (GCF)** of the numbers **32** and **20**, you can use several methods. Below, I'll demonstrate two common approaches: **listing factors** and the **Euclidean algorithm**.

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### Method 1: Listing the Factors

1. **List all factors of each number.**

- **Factors of 32:**  
     1, 2, 4, 8, 16, 32

- **Factors of 20:**  
     1, 2, 4, 5, 10, 20

2. **Identify the common factors.**

- Common factors of 32 and 20:  
     1, 2, 4

3. **Determine the greatest common factor.**

- The largest common factor is **4**.

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### Method 2: Euclidean Algorithm

The Euclidean algorithm is a systematic method for finding the GCF of two numbers.

1. **Divide the larger number by the smaller number and find the remainder.**

- 32 ÷ 20 = 1 with a remainder of **12**  
     (32 = 20 × 1 + 12)

2. **Replace the larger number with the smaller number and the smaller number with the remainder.**

- Now, find GCF of 20 and 12.

3. **Repeat the process.**

- 20 ÷ 12 = 1 with a remainder of **8**  
     (20 = 12 × 1 + 8)

- 12 ÷ 8 = 1 with a remainder of **4**  
     (12 = 8 × 1 + 4)

- 8 ÷ 4 = 2 with a remainder of **0**  
     (8 = 4 × 2 + 0)

4. **When the remainder is 0, the divisor at that step is the GCF.**

- The GCF is **4**.

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### Conclusion

Both methods yield the **Greatest Common Factor of 32 and 20 is 4**.
The GCF of 32 and 20 is 4.

What is the GCF of the two numbers below

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