What is the greatest common factor (GCF) of 36 and 48?

To determine the greatest common factor (GCF) of 36 and 48, we can start by finding the prime factorization of each number.

For 36, the prime factorization is:

• 36 = 2 x 2 x 3 x 3 = 2² x 3².

For 48, the prime factorization is:

• 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3¹.

Next, we identify the common prime factors and their lowest powers from both factorizations. The prime factors common to both numbers are 2 and 3.

In the factorization of 36 (2² x 3²) and 48 (2⁴ x 3¹), the lowest power of the common factors is:

• For 2, the minimum power is 2 (from 2²).

• For 3, the minimum power is 1 (from 3¹).

To find the GCF, we multiply these common factors together:

• GCF = 2² x 3¹ = 4 x 3 = 12.

Therefore, the greatest common factor of 36 and 48