# What is the greatest common monomial factor of 2a^2+12a?

May 24, 2015

$2 a$ is the greatest common monomial factor.

One way of seeing this is to completely factor each term first:

$2 {a}^{2} + 12 a = \left(2 \cdot a \cdot a\right) + \left(2 \cdot 2 \cdot 3 \cdot a\right)$

Both of these bracketed terms contains at least one factor $2$ and at least one factor $a$.

$= 2 a \cdot a + 2 a \cdot 6$

$= 2 a \cdot \left(a + 6\right)$