find GCF
15xy^2 and 25x^3y
You asked:
Find the polynomial greatest common divisor of the following expressions: \(15 y^{2} x\), \(25 x^{3} y\)
MathBot Answer:
The greatest common divisor is \(5 x y\).
Begin by factoring all expressions completely. $$\begin{aligned}15 y^{2} x &= 3\cdot 5 \cdot y^{2} \cdot x\\25 x^{3} y &= 5^{2} \cdot x^{3} \cdot y\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(15 y^{2} x, 25 x^{3} y) = 5\cdot (x)^{1}\cdot (y)^{1} = 5 x y\]