Question

What is the greatest common factor of 36 and 60?

Answer 1

To find the greatest common factor (GCF) of 36 and 60, we can start by finding the prime factorization of each number.

1. **Prime factorization of 36**:
- 36 can be divided by 2:
\( 36 \div 2 = 18 \)
\( 18 \div 2 = 9 \)
\( 9 \div 3 = 3 \)
\( 3 \div 3 = 1 \)
- Therefore, the prime factorization of 36 is:
\( 36 = 2^2 \times 3^2 \)

2. **Prime factorization of 60**:
- 60 can be divided by 2:
\( 60 \div 2 = 30 \)
\( 30 \div 2 = 15 \)
\( 15 \div 3 = 5 \)
\( 5 \div 5 = 1 \)
- Therefore, the prime factorization of 60 is:
\( 60 = 2^2 \times 3^1 \times 5^1 \)

3. **Finding the GCF**:
- We take the lowest power of all prime factors present in both factorizations:
- For the prime factor \( 2 \): the minimum power is \( 2^2 \).
- For the prime factor \( 3 \): the minimum power is \( 3^1 \).
- The prime factor \( 5 \) is not common to both numbers.

So, the GCF is:
\[
GCF = 2^2 \times 3^1 = 4 \times 3 = 12
\]

Thus, the greatest common factor of 36 and 60 is **12**.