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

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