Question

what is the gcf of $48m^{5}n$ and $81m^{2}n^{2}$?
○ $3mn$
○ $3m^{2}n$
○ $48m^{2}n$
○ $129m^{5}n^{2}$

Explanation:

Step1: Find GCF of coefficients

Prime factors of 48: $2^4 \times 3$
Prime factors of 81: $3^4$
GCF is $3$

Step2: Find GCF of $m$-terms

For $m^5$ and $m^2$, take lower exponent: $m^2$

Step3: Find GCF of $n$-terms

For $n^1$ and $n^2$, take lower exponent: $n^1 = n$

Step4: Multiply all GCF parts

$3 \times m^2 \times n$

Answer:

3m²n