What is the greatest common divisor of 36 and 60?

To find the greatest common divisor (GCD) of 36 and 60, we start by determining the prime factorizations of both numbers.

The prime factorization of 36 is:

• 36 can be divided by 2, giving 18.

• 18 can be divided by 2, giving 9.
• 9 can be divided by 3, giving 3.
• Lastly, 3 can be divided by 3, yielding 1. Thus, the prime factorization of 36 is (2^2 \times 3^2).

The prime factorization of 60 is:

• 60 can be divided by 2, giving 30.
• 30 can be divided by 2, giving 15.
• 15 can be divided by 3, giving 5.
• Finally, 5 is a prime number, yielding 1. Thus, the prime factorization of 60 is (2^2 \times 3^1 \times 5^1).

Next, we identify the common factors between these two factorizations:

• For the prime number 2, the minimum exponent in both factorizations is 2.
• For the prime