What is the greatest common factor (GCF) of 24 and 36?

To determine the greatest common factor (GCF) of 24 and 36, we first find the prime factorization of each number.

The prime factorization of 24 is:

• 24 = 2 × 2 × 2 × 3 = 2^3 × 3^1

The prime factorization of 36 is:

• 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2

Next, we identify the common prime factors and take the lowest power of each common factor:

• For the factor 2, the lowest power present is 2^2 (from 36).

• For the factor 3, the lowest power present is 3^1 (from both).

Now we multiply these common factors:

• GCF = 2^2 × 3^1 = 4 × 3 = 12

Thus, the greatest common factor of 24 and 36 is 12. This value represents the largest number that divides both 24 and 36 without leaving a remainder, confirming that option C is indeed correct.