What is the greatest common factor of 12 and 18?

What is the greatest common factor of 12 and 18?

• A. 3
• B. 6
• C. 4
• D. 12

Answer: (B)

Finding the greatest common factor means identifying the largest number that divides both numbers without a remainder. For 12 and 18, look at their prime factorizations: 12 = 2^2 × 3 and 18 = 2 × 3^2. The common prime factors are 2 and 3, so take the smallest powers that appear in both: 2^1 × 3^1 = 6. Therefore, 6 is the largest number that divides both. The other options don’t fit because 4 doesn’t divide 18, 12 doesn’t divide 18, and 3 is smaller than 6 even though it does divide both.

Finding the greatest common factor means identifying the largest number that divides both numbers without a remainder. For 12 and 18, look at their prime factorizations: 12 = 2^2 × 3 and 18 = 2 × 3^2. The common prime factors are 2 and 3, so take the smallest powers that appear in both: 2^1 × 3^1 = 6. Therefore, 6 is the largest number that divides both. The other options don’t fit because 4 doesn’t divide 18, 12 doesn’t divide 18, and 3 is smaller than 6 even though it does divide both.