Find the greatest common factor of 12x^3 and 18x^2.

Find the greatest common factor of 12x^3 and 18x^2.

• A. 12x^2
• B. 6x^2
• C. 6x^3
• D. 18x^2

Answer: (B)

The greatest common factor is the largest expression that divides both terms. Start by factoring each term: 12x^3 has numeric factors 2^2 and 3, and x^3; 18x^2 has numeric factors 2 and 3^2, and x^2. For the common part, take the smallest powers: 2^1, 3^1, and x^2. Multiply these together to get 2 * 3 * x^2 = 6x^2. This factor divides both original expressions (12x^3 ÷ 6x^2 = 2x and 18x^2 ÷ 6x^2 = 3), and you can’t go any larger because extending any part would fail to divide one of the terms. So the greatest common factor is 6x^2.

The greatest common factor is the largest expression that divides both terms. Start by factoring each term: 12x^3 has numeric factors 2^2 and 3, and x^3; 18x^2 has numeric factors 2 and 3^2, and x^2. For the common part, take the smallest powers: 2^1, 3^1, and x^2. Multiply these together to get 2 * 3 * x^2 = 6x^2. This factor divides both original expressions (12x^3 ÷ 6x^2 = 2x and 18x^2 ÷ 6x^2 = 3), and you can’t go any larger because extending any part would fail to divide one of the terms. So the greatest common factor is 6x^2.