Question

question identify the greatest common factor of 40a^3b^3 and 32a^3.

Explanation:

Step1: Find GCF of coefficients

Find GCF of 40 and 32. Prime - factorize: $40 = 2\times2\times2\times5$, $32 = 2\times2\times2\times2\times2$. The common factors are $2\times2\times2=8$.

Step2: Find GCF of variable parts

For the variable part $a^{3}b^{3}$ and $a^{3}$, the common variable factor is $a^{3}$ (since the lowest power of $a$ is 3 in both terms and $b$ is not present in the second - term).

Step3: Combine GCF of coefficients and variables

The GCF of $40a^{3}b^{3}$ and $32a^{3}$ is the product of the GCF of the coefficients and the GCF of the variable parts, which is $8a^{3}$.

Answer:

$8a^{3}$