How do you find the GCF of 42a^2b, 6a^2, 18a^3?

Nov 30, 2017

Greatest Common Factor ( GCF ) of the three algebraic expressions given is equal to $\textcolor{red}{6 {a}^{2}}$

Explanation:

The Highest Common Factor (HCF) or the Greatest Common Factor (GCF) of algebraic expressions is obtained in a similar way to the method used for numbers.

Write the factors of $42 {a}^{2} b = \left(7 \cdot 2 \cdot 3 \cdot a \cdot a \cdot b\right)$
Write the factors of $6 {a}^{2} = \left(2 \cdot 3 \cdot a \cdot a\right)$
Write the factors of $18 {a}^{3} = \left(2 \cdot 3 \cdot 3 \cdot a \cdot a \cdot a\right)$

We observe that the common factors are $\left(2 \cdot 3 \cdot a \cdot a\right)$

Hence, GCF = Product of common factors = $\textcolor{red}{6 {a}^{2}}$

I hope this procedure helps.