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

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

The prime factorization of 24 is:

• 24 = 2 × 2 × 2 × 3 = (2^3 \times 3^1).

The prime factorization of 36 is:

• 36 = 2 × 2 × 3 × 3 = (2^2 \times 3^2).

Once we have both factorizations, the next step is to identify the common prime factors and take the lowest power of each common factor.

The common prime factors between 24 and 36 are 2 and 3.

• For the factor of 2, the lowest power between (2^3) and (2^2) is (2^2).

• For the factor of 3, the lowest power between (3^1) and (3^2) is (3^1).

Next, we multiply these together to find the GCF:

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GCF = 2^2 \times 3^1 = 4 \times 3 = 12