How do you find the gcf of 8a^2b + 4ab - 12ab^2?

Jul 1, 2015

Find the largest number and highest degree of each variable that can be divided evenly into the expression.

Explanation:

$8 {a}^{2} b + 4 a b - 12 a {b}^{2}$

Largest number = $4$
Highest degree of $a$ = $a$
Highest degree of $b$ = $b$

Multiply the results to get the GCF of $4 a b$.

Factor out $4 a b$.

$4 a b \left(2 a + 1 - 3 b\right)$

Jul 1, 2015

gcf (Greatest Common Factor) of 8a^2b+4ab−12ab^2 is $4 a b$

Explanation:

Factoring each term independently:
$8 {a}^{2} b = 2 \times 2 \times 2 \times a \times a \times b$
$4 a b = 2 \times 2 \times a \times b$
$12 a {b}^{2} = 2 \times 2 \times 3 \times a \times b \times b$

Extracting the factors common to all three terms:
$2 \times 2 \times a \times b = 4 a b$