Find the greatest common factor of 10ab^2x^2 and 15a^2by^2
You asked:
Find the polynomial greatest common divisor of the following expressions: \(10 b^{2} x^{2} a\), \(15 a^{2} y^{2} b\)
MathBot Answer:
The greatest common divisor is \(5 a b\).
Begin by factoring all expressions completely. $$\begin{aligned}10 b^{2} x^{2} a &= 2\cdot 5 \cdot b^{2} \cdot x^{2} \cdot a\\15 a^{2} y^{2} b &= 3\cdot 5 \cdot a^{2} \cdot y^{2} \cdot b\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(10 b^{2} x^{2} a, 15 a^{2} y^{2} b) = 5\cdot (a)^{1}\cdot (b)^{1} = 5 a b\]