Question

How do you find the GCF of `24cd^3, 48c^2d`?

Answer 1

See a solution process below:

Explanation:

First, we can write the prime factor for each term as:

`24cd^3 = 2 xx 2 xx 2 xx 3 xx c xx d xx d xx d`

`48c^2d = 2 xx 2 xx 2 xx 2 xx 3 xx c xx c xx d`

The common prime factors are:

`24cd^3 = color(red)(2) xx color(red)(2) xx color(red)(2) xx color(red)(3) xx color(red)(c) xx color(red)(d) xx d xx d`

`48c^2d = color(red)(2) xx color(red)(2) xx color(red)(2) xx 2 xx color(red)(3) xx color(red)(c) xx c xx color(red)(d)`

Therefore the Greatest Common Factor is:

`"GCF" = color(red)(2) xx color(red)(2) xx color(red)(2) xx color(red)(3) xx color(red)(c) xx color(red)(d) = 24cd`