Question

find the greatest common factor. 3f³, 6f² write your answer as a constant times a product of single variables raised to exponents.

Explanation:

Step1: Find GCF of coefficients

The coefficients are 3 and 6. The GCF of 3 and 6 is 3, since 3 is the largest number that divides both 3 and 6.

Step2: Find GCF of variables

For the variable part, we have \( f^3 \) and \( f^2 \). Using the rule that the GCF of \( f^m \) and \( f^n \) (where \( m \geq n \)) is \( f^n \), here \( m = 3 \), \( n = 2 \), so the GCF of \( f^3 \) and \( f^2 \) is \( f^2 \).

Step3: Combine the results

Multiply the GCF of the coefficients and the GCF of the variables. So, \( 3\times f^2 = 3f^2 \).

Answer:

\( 3f^2 \)