Question

find the greatest common factor of $6b^{3}$ and $15a^{4}$.

Explanation:

Step1: Factorize the coefficients

Factorize 6 and 15.
$6 = 2\times3$
$15 = 3\times5$
The common factor of 6 and 15 is 3.

Step2: Analyze the variables

For the variable part, $6b^{3}$ has $b^{3}$ and $15a^{4}$ has $a^{4}$. There are no common variables between them (since one has \(b\) and the other has \(a\), and they are different variables). So the variable part of the GCF is 1 (since there's no common variable factor).

Step3: Combine the common factors

Multiply the common coefficient factor and the common variable factor. The common coefficient factor is 3, and the common variable factor is 1. So the GCF is \(3\times1 = 3\).

Answer:

3