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

• A. 6
• B. 8
• C. 10
• D. 12

Answer: (D)

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To find the GCD of 36 and 60, we can utilize the prime factorization method.

First, we prime factorize both numbers:

• The prime factorization of 36 is:

(36 = 2^2 \times 3^2)

• The prime factorization of 60 is:

(60 = 2^2 \times 3^1 \times 5^1)

Next, we identify the common prime factors between the two factorizations. The common prime factors are 2 and 3.

Now, we take the lowest power of each common prime factor:

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

• For the prime factor 3, the minimum exponent is 1.

Thus, the GCD can be calculated by multiplying these common prime factors raised to their respective lowest powers:

GCD = (2^2 \times 3^1 = 4 \times 3 = 12)

Therefore, the greatest common divisor of 36 and 60 is 12. This