What is the greatest common factor of 36 and 60?

To determine the greatest common factor (GCF) of 36 and 60, it's important to first find the prime factorization of each number.

The prime factorization of 36 is:

• 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2

The prime factorization of 60 is:

• 60 = 2 × 2 × 3 × 5 = 2^2 × 3 × 5

Next, to find the GCF, identify the lowest powers of all prime factors that are present in both factorizations.

For the number 2, the lowest power between 36 and 60 is 2^2. For the number 3, the lowest power is 3^1. The factor 5 appears only in the prime factorization of 60 and is not considered.

Now, multiply these together to find the GCF: GCF = 2^2 × 3^1 = 4 × 3 = 12.

This shows that the greatest common factor of 36 and 60 is indeed 12. Hence, the correct answer reflects a proper understanding of prime factorization and the