Regarding GCF factoring, can the same answer be derived from multiple number sets? Specifically fin the following problem:

$\displaystyle 40a^5x+80a^5y-120a^5z$ & its answer 40a^5(x + 2y - 3z)

40 obviously is the GCF and goes into all three numbers. But what if one doesn't realize this initially and decides to approach it as such?

pulling out the terms

$\displaystyle 40a^5x = 2^2*10$

$\displaystyle 80a^5y=2^4*5$

$\displaystyle -120a^5z= 2^3*15$

then finding the lowest power of each variable and number. Will one still arrive at the same answer as if they used 40 as the GCF?