Find the greatest common factor of 18 and 24.

Find the greatest common factor of 18 and 24.

• A. 6
• B. 3
• C. 12
• D. 18

Answer: (A)

Finding the greatest common factor means finding the largest number that can divide both numbers exactly. A clear way is to list all the factors of each number and see which ones they share. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common factors are 1, 2, 3, and 6, and among these the largest is 6. You can also see this from prime factorization: 18 = 2 × 3^2 and 24 = 2^3 × 3. The common primes with the smallest powers are 2^1 and 3^1, which multiply to 6. So, the greatest common factor is 6.

Finding the greatest common factor means finding the largest number that can divide both numbers exactly. A clear way is to list all the factors of each number and see which ones they share.

The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common factors are 1, 2, 3, and 6, and among these the largest is 6.

You can also see this from prime factorization: 18 = 2 × 3^2 and 24 = 2^3 × 3. The common primes with the smallest powers are 2^1 and 3^1, which multiply to 6.

So, the greatest common factor is 6.