Find the greatest common factor of 16a^3x^4y,40a^2y^2x and 28ax^2
You asked:
Find the polynomial greatest common divisor of the following expressions: \(16 a^{3} x^{4} y\), \(40 a^{2} y^{2} x\), \(28 x^{2} a\)
MathBot Answer:
The greatest common divisor is \(4 a x\).
Begin by factoring all expressions completely. $$\begin{aligned}16 a^{3} x^{4} y &= 2^{4} \cdot a^{3} \cdot x^{4} \cdot y\\40 a^{2} y^{2} x &= 2^{3}\cdot 5 \cdot a^{2} \cdot y^{2} \cdot x\\28 x^{2} a &= 2^{2}\cdot 7 \cdot x^{2} \cdot a\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(16 a^{3} x^{4} y, 40 a^{2} y^{2} x, 28 x^{2} a) = 2^{2}\cdot (a)^{1}\cdot (x)^{1} = 4 a x\]