What is the greatest common divisor of 36 and 60?

What is the greatest common divisor of 36 and 60?

• A. 6
• B. 12
• C. 18
• D. 24

Answer: (B)

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

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