What is the largest number that will divide both 18 and 24 perfectly, with no remainder?

• A. 3
• B. 6
• C. 9
• D. 12

Answer: (B)

Finding the greatest common divisor of two numbers is what this asks you to do. It’s the largest number that can divide both numbers with no remainder. Factor the numbers: 18 = 2 × 3^2 and 24 = 2^3 × 3. The common prime factors are 2 and 3, with the smallest powers that appear in both, giving 2^1 × 3^1 = 6. So 6 is the biggest number that divides both. The other options don’t fit: 3 is a common divisor but smaller; 9 divides 18 but not 24; 12 divides 24 but not 18.