What is the greatest common factor of 36 and 48?

• A. 6
• B. 18
• C. 12
• D. 24

Answer: (C)

Finding the greatest common factor means identifying the largest number that divides both 36 and 48 without a remainder. Do this by prime factorization: 36 = 2^2 × 3^2, and 48 = 2^4 × 3. For the common factors, use the smallest powers of the primes that appear in both factorizations: 2^2 and 3^1. Multiply them to get 2^2 × 3 = 4 × 3 = 12. This 12 divides both numbers, and any larger number would fail to divide at least one of them, so 12 is the greatest common factor. For quick check, 24 doesn’t divide 36, 18 doesn’t divide 48, and 6 is smaller than 12, so 12 is the largest common divisor.