What is the greatest common divisor (GCD) of 24 and 36?

To find the greatest common divisor (GCD) of 24 and 36, we start by determining the prime factorization of both numbers.

For 24, the prime factorization is:

• 24 = 2 × 12

• 12 = 2 × 6

• 6 = 2 × 3

Thus, the complete prime factorization of 24 is (2^3 \times 3^1).

For 36, the prime factorization is:

• 36 = 6 × 6

• 6 = 2 × 3

Thus, the complete prime factorization of 36 is (2^2 \times 3^2).

To find the GCD, we take the lowest power of each prime that appears in the factorizations:

• For the prime number 2: The lowest power is (2^2) (from the factorization of 36).

• For the prime number 3: The lowest power is (3^1) (from the factorization of 24).

Now, we multiply these together:

GCD = (2^2 \times 3^1 = 4 \times 3 =