## How to use the distributive property to factor out the greatest common factor | Khan Academy

– [Voiceover] We’re asked

to apply the distributive property to factor out the

greatest common factor, and we have 35 plus 50 is equal to, so let me get my scratch pad out. So we have 35 plus 50 is equal to, now what is the greatest

common factor of 35 and 50. So what’s the largest whole number that’s divisible into both of these. Well I could write 35 as, let’s see, I could write that as five times seven, and I could write 50 as five times ten, and so we see five is the

greatest common factor. Seven and ten don’t have

any factors in common. So I could rewrite this, I could write 35 as

equal to five times seven and I could rewrite 50 as equal to, get another color here, I could rewrite 50 as five times ten, and of course, I’m adding them, so I have plus right over here. If I want, I could put parentheses, but order of operations would make me do the multiplication first, anyway. But now I want to factor out

that greatest common factor. I want to factor out the five. So what I’m really doing right over here is I’m unwinding the

distributive property. So if I factor out a five,

this is going to be equal to, this is going to be equal to

let’s factor out the five. Five times, so you do 35 divided by five, you’re just left with the seven. You’re just left with the seven over here. So you’re just left with the seven after you’ve factored out the five, and over here, you’re

just left with the ten. So five, or seven plus ten, and we’re done. 35 plus 50 is equal to

five times seven plus ten. So let me now go and type that in. So this is the same thing as five, five times seven plus ten. And you know you’ve factored out the greatest common factor because seven and ten don’t have any

factors in common anymore. They’re called relatively prime. They have no factors in

common other than one. So we could now check that. Let’s do a couple more of these. Apply the distributive

property to factor out the greatest common factor. So let’s see if we can just do

this one a little bit faster. So let’s see, the largest

number it’s divisible, in both 75 and 20, I don’t

know, let me try five. So if I say five times,

so 75 divided by five, let’s see is going to

be, it’s going to be 15. Is that right? Yeah, cause five times ten

is 50, five times five is 25. Yeah, so it’s 15, and I got that 15 by dividing 75 by five. So 15 plus, and then 20

divided by five would be, 20 divided by five would be four. 15 plus four. Let’s see, did I do this right? 15 and four don’t have

any factors in common, and if I were to apply the

distributive property here, I’d have five times 15 is 75. Five times four is 20. Yeah, I’m feeling good about that. We got it right.

## Esther Meeks

Sep 9, 2015, 11:52 pmThank you!!!!!!!

## Sonia Aguilar

Oct 10, 2015, 11:08 pmOMG!!! I GET IT KNOW THANKS YOU EXPLAIN BETTER THAN MY MATH TEACHER!!

## Plump

Dec 12, 2015, 7:44 pmThanks M8!

## Kyasia Jordan

Jan 1, 2016, 5:47 pmOmg! It really worked thanks so much

## Raul Restrepo

Feb 2, 2016, 11:29 pmThank you so much with out you my life would be a struggle everyday

## Evelyn Reyes

Feb 2, 2016, 10:46 pmTHank YOu

## Neon Valor

Feb 2, 2016, 11:45 pmThanks m8, helped a lot on my hw! ๐

## laughalot 21

Mar 3, 2016, 11:07 pmi

## Chris Halikas

Apr 4, 2016, 4:20 amWhat does he use to draw?

## ๊นํ์ฑ

Jul 7, 2016, 12:43 amhey thx dude

## sunny shin

Sep 9, 2016, 4:13 amWOOH!!! You changed your back round!!!

## Kit Daley

Sep 9, 2016, 2:58 amVery useful, helped me with my homework. ๐

## omar ramos

Sep 9, 2016, 8:29 pmThank you bro you don't know how much you've helped

## kelly Sanchez

Sep 9, 2016, 2:51 amthanks for the video. big homework saver

## VXXYC

Oct 10, 2016, 9:38 pmvery helpful especially for a 6th grader like me on my homework

## Tito Rays

Nov 11, 2016, 11:37 pmIm in 3rd grade and i do these things xD

## Daweigh Fair

May 5, 2017, 1:33 pmThanks

## Just Paige

Aug 8, 2017, 1:20 amTHANKS SO MUCH! You did better then my teacher!

## mercyAF

Aug 8, 2017, 1:40 am10 isn't prime …

## Omarion Gore

Oct 10, 2017, 12:52 pmhey

## Destiny cheyenne

Dec 12, 2018, 11:01 pmSooooo thankful for this, best explanation I have ever seen

## Savannah Rodriguez

Sep 9, 2019, 11:46 pmwhere did you get the 7 from?