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