Question

How do you find the GCF of `8c^2d^3, 16c^3d`?

Answer 1

See a solution process below:

Explanation:

Find the prime factors for each number as:

`8c^2d^3 = 2 xx 2 xx 2 xx c xx c xx d xx d xx d`

`36 = 2 xx 2 xx 2 xx 2 xx c xx c xx c xx d`

Now identify the common factors and determine the GCF:

`8c^2d^3 = color(red)(2) xx color(red)(2) xx color(red)(2) xx color(red)(c) xx color(red)(c) xx color(red)(d) xx d xx d`

`36 = color(red)(2) xx color(red)(2) xx color(red)(2) xx 2 xx color(red)(c) xx color(red)(c) xx c xx color(red)(d)`

Therefore:

`"GCF" = color(red)(2) xx color(red)(2) xx color(red)(2) xx color(red)(c) xx color(red)(c) xx color(red)(d) = 8c^2d`