What is the largest number that will divide both 24 and 36 perfectly, with no remainder?

• A. 6
• B. 12
• C. 18
• D. 24

Answer: (B)

This is about finding the greatest common divisor—the largest number that divides both 24 and 36 evenly. A clear way to see it is by prime factorization: 24 = 2^3 × 3 and 36 = 2^2 × 3^2. The common prime factors are 2 and 3, and we take the smallest powers that appear in both numbers, giving 2^2 × 3 = 4 × 3 = 12. So the largest number that divides both without a remainder is 12.

You can also check with the Euclidean method: 36 = 24 × 1 + 12, then 24 = 12 × 2 + 0, confirming the gcd is 12.

Other numbers mentioned wouldn’t work as the greatest common divisor: 24 doesn’t divide 36, and 18 doesn’t divide 24, while 6 divides both but is smaller than 12.