Find the greatest common factor of a^2x^2,6axy^2 and 9ay^2
You asked:
Find the polynomial greatest common divisor of the following expressions: \(a^{2} x^{2}\), \(6 y^{2} a x\), \(9 y^{2} a\)
MathBot Answer:
The greatest common divisor is \(a\).
Begin by factoring all expressions completely. $$\begin{aligned}a^{2} x^{2} &= a^{2} \cdot x^{2}\\6 y^{2} a x &= 2\cdot 3 \cdot y^{2} \cdot a \cdot x\\9 y^{2} a &= 3^{2} \cdot y^{2} \cdot a\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(a^{2} x^{2}, 6 y^{2} a x, 9 y^{2} a) = (a)^{1} = a\]