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## Pre-algebra

### Course: Pre-algebra > Unit 1

Lesson 1: Factors and multiples# Understanding factor pairs

Use multiplication and an understanding of area to identify factor pairs for 6 and 16. Created by Sal Khan.

## Want to join the conversation?

- Do you have to memorize the multipication table to get good at factor pairs?(16 votes)
- Yes, memorizing the multiplication table helps you get good at factor pairs. If you don’t have the multiplication table fully memorized, you can use strategies to help you with forgotten facts. Example: suppose you know that 7x7 is 49 but you forget 7x8. You can just add 49+7 to get 56.

There are also some tests you can use, to find factors.

If the last digit is 0, 2, 4, 6, or 8, then 2 is a factor.

If the digits add to a multiple of 3, then 3 is a factor.

If the last two digits form a multiple or 4, then 4 is a factor.

If the last digit is 0 or 5, then 5 is a factor.

If 2 and 3 are factors, then so is 6.

If the last three digits form a multiple of 8, then 8 is a factor.

If the digits add to a multiple of 9, then 9 is a factor.

If the last digit is 0, then 10 is a factor.

Have a blessed, wonderful day!(27 votes)

- is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300 is a factor of 300 does that make sense?(10 votes)
- Yes, all of those numbers are factors of 300.(11 votes)

- Still do not understand factor pairs(12 votes)
- me niether and im 56 years old(2 votes)

- can i get 10 up votes(9 votes)
- maybe.... i'll upvote U if U upvote me on "can there be three factors in a factor pair?"(5 votes)

- Video transcript

- What we're going to do in this video is talk about factors and factor pairs. Now when we talk about factors, these are really numbers that can be multiplied together to make some number. So, for example, if I were to talk about factors of six, I could multiply two times three to get six and so we would say that two and three are factors of six. In fact we would also say that two and three is a factor pair for six 'cause when I multiply those two I can get six. Now to think about all of the different factor pairs for a number we could think about it in terms of area. How can we make a rectangle with area six? Well you could do it if it's two units by three units. So it could look something like this, I'll just hand draw it. So let's say it has, so let's say our rectangle looks like this. So it has two rows and then three columns and lets say these all have equal area, it's hand drawn but you can see that the area here would be two times three, which would be equal to six square units. Now, what if, what are other(10 votes) - How can I remember which is a Multiple and which is a Factor?(7 votes)
- a multiple is the answer (20 is a multiple of 5 times 4) 5 times 4 = 20(5 votes)

- can i get 10 up votes(9 votes)
- can i get 10 up votes-your last comment(0 votes)

- can there be three factors in a factor pair?(7 votes)
- Well, they're called pairs...

It's easiest as a pair because if you know a factor of a number, you can just divide the number by the factor to get another factor.

Anyway, you could have a factor triplet if you broke one of the 2 factors in the pair into 2 smaller factors haha

This leads on to the idea of prime factorisation, which is quite interesting.(1 vote)

- ummm I am guessing you people in 5th grade(5 votes)
- I am in 3rd grade doing pre- algebra what about you noob(3 votes)

- im honestly jealous, i wish sal was my teacher those 30ish years ago. maybe i wouldn't be here trying to learn what i wasn't taught long ago.(4 votes)

## Video transcript

- What we're going to do in this video is talk about factors and factor pairs. Now when we talk about factors, these are really numbers that
can be multiplied together to make some number. So, for example, if I were
to talk about factors of six, I could multiply two
times three to get six and so we would say that two
and three are factors of six. In fact we would also
say that two and three is a factor pair for six
'cause when I multiply those two I can get six. Now to think about all of
the different factor pairs for a number we could think
about it in terms of area. How can we make a rectangle with area six? Well you could do it if it's
two units by three units. So it could look something like this, I'll just hand draw it. So let's say it has, so
let's say our rectangle looks like this. So it has two rows and then three columns and lets say these all have equal area, it's hand drawn but you
can see that the area here would be two times three,
which would be equal to six square units. Now, what if, what are other
ways to get to an area of six? Well you could have
something that is one row but then it has six columns. So maybe it looks something like this. It looks like this. So it's one row and then
you have one, two, three, four, five, and I want them all
to be roughly the same size. So it's one times six would
be also an area of six so that would be another factor pair. We know that two times
three is equal to six and we know that one
times six is equal to six and these are actually the
two factor pairs for six and we can do it with larger numbers. We could think about what
about all the factor pairs for something like 16? Pause this video and see if
you can think about that. Well I'll set up a little
table here to think about that and so in this column
I'll put the first factor and in this column I'll
put the second factor and the way I like to
do it is I start at one and I keep working up, up to the number, to try to figure out all of the factors. So let's start with one. So one is definitely divisible into 16 and as long as you put
a whole number here it's going to be divisible by one
and we don't have to multiply by one to get to 16, we'll
have to multiply it by 16 so that's a factor pair
right there, one and 16. Now what about two? Does two go into 16? Well sure, two times eight is 16 so that's another factor pair. Two times eight. We found another factor pair. Now what about three? Does three go evenly into 16? Well no, three times five is 15 and three times six is 18
so three doesn't go into 16 so three would not be a factor of 16. What about four? Well four times four is 16 so
that's a factor pair there. Four and four. What about five? Well no, five times two is
10, five times three is 15, five times four is 20. Five does not go evenly into 16. Same thing for six, six times two is 12, six times three is 18,
does not go evenly into 16. What about seven? Seven does not evenly go into 16. Seven times two is 14,
seven times three is 21. What about eight? Well we already know that
eight goes evenly into 16, you might be tempted to say
oh there's another factor pair of eight times two but we
already wrote that down. We just happened to say
that two is the first factor and eight is the second
factor but you could say it the other way around
so we don't have to then go to eight times two. And once you've gone half
way you can be confident that you've already found
all the factor pairs because then you could go to nine, nine doesn't go into it,
10, 11, 12, 13, 14, 15 but then 16, of course, is divisible by 16 but we've already written
that here in this factor pair. So we have these three factor pairs, one and 16, two and
eight and four and four.