About this video
Sal uses the distributive property in reverse to factor out the greatest common factor from a sum. He rewrites 35 + 50 as 5 x (7 + 10) and 75 + 20 as 5 x (15 + 4), and checks that the numbers left in the brackets have no common factors other than 1.
You'll be able to
- find the greatest common factor of two numbers in a sum.
- factor out the GCF to rewrite a sum like 35 + 50 as 5 x (7 + 10).
- check my factoring by distributing back or by making sure the numbers in brackets are relatively prime.
Key words
- greatest common factor (GCF)
- The largest whole number that divides into both numbers.
- distributive property
- a x (b + c) = a x b + a x c; multiplying a sum is the same as multiplying each part and adding.
- factor out
- To pull a common factor outside brackets, undoing the distributive property.
- relatively prime
- Numbers that have no common factors other than 1, like 7 and 10.
Transcript
- [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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