What is the greatest common factor of 8 and 12?

What is the greatest common factor of 8 and 12?

• A. 2
• B. 6
• C. 4
• D. 8

Answer: (C)

The greatest common factor is the largest number that evenly divides both numbers. For 8 and 12, common divisors include 1, 2, and 4, and there isn’t a larger number that divides both. A quick check with prime factors confirms this: 8 is 2^3 and 12 is 2^2 × 3, so the common prime factor is 2 with the smallest shared power being 2^2, which equals 4. Therefore, the greatest common factor is 4.

The greatest common factor is the largest number that evenly divides both numbers. For 8 and 12, common divisors include 1, 2, and 4, and there isn’t a larger number that divides both. A quick check with prime factors confirms this: 8 is 2^3 and 12 is 2^2 × 3, so the common prime factor is 2 with the smallest shared power being 2^2, which equals 4. Therefore, the greatest common factor is 4.