Question

How do you write `30 + 54` as the sum of two numbers times their GCF?

Answer 1

See a solution process below:

Explanation:

Find the prime factors for each number as:

`30 = 2 xx 3 xx 5`

`54 = 2 xx 3 xx 3 xx 3`

Now identify the common factors and determine the GCF:

`30 = color(red)(2) xx color(red)(3) xx 5`

`54 = color(red)(2) xx color(red)(3) xx 3 xx 3`

Therefore:

`"GCF" = color(red)(2) xx color(red)(3) = 6`

Now, we can factor `color(red)(6)` from each number giving:

`(color(red)(6) xx 5) + (color(red)(6) xx 9) =>`

`color(red)(6)(5 + 9)`

Answer 2

`84 = 6 xx (7 + 7)`
Or, completely written out:
`30 + 54 = 6 xx (7 + 7)`

Explanation:

First, we find their Greatest Common Factor:
`30 = 2 xx 3 xx 5`
`54 = 2 xx 3 xx 3 xx 3`
`GCF = 6`

The sum of the two numbers is `30 + 54 = 84`
Divide by the GCF to get a multiplicative factor easily:

`84/6 = 14` We convert `14` into a simple sum:
`14 = 7 + 7` and then combine them into the final expression.
`84 = 6 xx (7 + 7)`