Find the greatest common factor of 18 and 24.

• A. 6
• B. 12
• C. 3
• D. 18

Answer: (A)

The idea here is to find the greatest common factor, the largest number that divides both numbers evenly. Using prime factorization, 18 can be written as 2 × 3^2 and 24 as 2^3 × 3. The common factors come from the primes they share, taking the smallest powers: 2^1 and 3^1, which multiply to 6. So 6 goes into both numbers without a remainder, and there isn’t a larger number that does that for both. For example, 12 isn’t a divisor of 18, and 18 isn’t a divisor of 24, so they aren’t common factors. 3 is a common factor, but it’s smaller than 6. Therefore, the greatest common factor is 6.