What is the greatest common divisor (GCD) of 36 and 60?

To determine the greatest common divisor (GCD) of 36 and 60, it's helpful to first identify the prime factorization of each number.

For 36:

• 36 can be factored into (2^2 \times 3^2).

For 60:

• 60 can be factored into (2^2 \times 3^1 \times 5^1).

The GCD is found by taking the lowest power of all prime factors common to both numbers.

• The prime factor 2 appears as (2^2) in both factorizations, so we take (2^2).

• The prime factor 3 appears as (3^2) in 36 and (3^1) in 60, so we take (3^1).

• The prime factor 5 appears only in 60, so it is not included in the GCD.

Now, we multiply these together:

[

GCD = 2^2 \times 3^1 = 4 \times 3 = 12.

]

Thus, the GCD of 36 and 60 is 12, confirming that this option is accurate