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### Course: Pre-algebra > Unit 1

Lesson 1: Factors and multiples# Finding factors and multiples

Sal uses divisibility rules to determine if numbers are factors of 154 and then finds multiples of 14. Created by Sal Khan.

## Want to join the conversation?

- what is a multiple? can someone please clarify the difference between a multiple and a factor?(32 votes)
- Multiples and factors are opposite terms.

Multiplies of a number are the numbers that appear when you create a multiplication table for a number. For example:

Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, etc.

Each multiple is created by multiply 5 times some other number.

Factors are the numbers used to create a multiple.

Factors of 15 are:

3 and 5 because 3 x 5 = 15

1 and 15 because 1 x 15 = 15

Hope this helps.(87 votes)

- What is a factor and what is a multiple?(10 votes)
- factor- a number or quantity that when multiplied with another produces a given number or expression.

multiple-a number that can be divided by another number without a remainder.(19 votes)

- is there an easier way to do this?(16 votes)
- There are a lot of tricks you can use, as Sal does in most of these videos. If you search up
**divisibility tricks**you might find some!(7 votes)

- I still do not understand factors can someone pls explain?(10 votes)
- A factor is one of the numbers in division - the answer is called a "product" while the numbers being multiplied together are called "factors."(7 votes)

- i have a hard time knowing the difference between factors and multiples.(7 votes)
- Factor is a whole number which you can divide or get by dividing a certain number with while a multiple is a whole number you can get by multiplying a certain number.

For example: Let's have a certain number 18.

It's factors are:

1, 2, 3, 9, 18

While it's multiples are:

18, 36, 54, 72, 90 ... and so on.

Hope this helps.(5 votes)

- how do I know if a number is divisible by 7?(7 votes)
- To check if a number is evenly divisible b 7: Take the last digit of a number, double it (x2). Then subtract the result from the rest of the number. I f the resulting number is evenly divisible by 7 so is the original number OR SIMPLY DIVIDE IT AND SEE IN SHORT(5 votes)

- When the number can be divided by 2 and 7 can then be concluded that the number can also be divided by 14? Thanks in advance!(4 votes)
- Why does the trick of adding the numbers of the multiple not work for 5? The multiple 154 comes out to 10, so the factor 5 should be a factor of 154. Why is it not a factor?(5 votes)
- Good question!

One way to see why the digit addition doesn't work for`5`

:

Listing the multiples of`5`

, notice what happens when you sum their digits.

5 -> 5

10 -> 1

15 -> 6

20 -> 2

25 -> 7

30 -> 3

The sum of digits doesn't really have any meaningful pattern to it.

However, you can see that the ones digit of all the multiples is either`5`

or`0`

, indicating to us the divisibility rule for`5`

: The ones digit is`5`

or`0`

.

We can then tell that`5`

is not a factor of`154`

- the ones digit of`154`

is`4`

.

Happy learning!(2 votes)

- is there a ezer way to do this 🤔(4 votes)
- Yes you use the divisibility rules(0 votes)

- can all the numbers be divisible(2 votes)
- All numbers are divisible by themselves and divisible by 1, but most numbers have more than those two factors.

Prime numbers only have two factors, themselves and 1.

Composite numbers have more than two factors.

Every number is either prime or composite, the exception being 1. 1 only has one factor, itself.(3 votes)

## Video transcript

Which of the following
numbers is a factor of 154? So when a number is going
to be a factor of 154 is if we can divide
that number into 154 and not have a remainder. Or another way of thinking
about it-- a number is a factor of 154 if 154 is
a multiple of that number. So let's look at each of these
and see which of these we can rule out or say is a factor. So does 3 divide
evenly into 154? Or, another way of
thinking about it, is 154 a multiple of 3? Well you'll later learn
that you could actually test whether something
is divisible by 3 by adding up the digits. And if that's divisible
by 3, then it's going to be divisible by 3. And so you see
here, 1 plus 5 is 6. 6 plus 4 is 10. 10 is not divisible by 3. But if you didn't want
to do that little trick-- and we have other
videos where we go into more detail
about that trick-- you can actually just
divide 3 into 154. 3 doesn't go into 1. It does go into 15 five times. 5 times 3 is 15. Subtract. Then we have 0. Then you bring down a 4. 3 goes into 4 one time. 1 times 3 is 3. Subtract, and you
have a remainder of 1. So 3 is clearly not a factor of
154, so we can rule that out. Now what about 5? Well, any multiple
of 5 is either going to have 5 or
0 in the ones place. You see that if we write 5
times 1 is 5, 5 times 2 is 10, 5 times 3 is 15, 5 times 4 is
20, you either have a 5 or a 0 in the ones place. This does not have 5
or a 0 the ones place, so it's not going to
be divisible by 5. 5 is not a factor. 154 is not a multiple of 5. Now 6 is interesting. You could do the same thing. You could try to
divide 6 into 154. But if something
is divisible by 6, it's definitely going to
be divisible by 3 as well because 6 is divisible by 3. So we can immediately
rule this one out as well. Because 154 is not
divisible by 3, it's also not going
to be divisible by 6. And you could try
it out if you like. And we could make the
same argument for 9. If something is divisible by 9,
it's going to be divisible by 3 because 9 is divisible by 3. Well, it's not
divisible by 3, so we're going to rule out 9 as well. So we've ruled out everything. It looks like 14
is our only option, but let's actually verify it. Let's actually
divide 14 into 154. 14 doesn't go into 1. It goes into 15
exactly one time. 1 times 14 is 14. We subtract. We get 1. Bring down the 4. 14 goes into 14 one time. 1 times 14 is 14. And of course, we
have no remainder. So 14 goes into 154
exactly 11 times. Or 11 times 14 is 154. 154 is a multiple of 14. Let's do one more. Which of the following
numbers is a multiple of 14? So now we have 14,
and we're trying to think of its multiples. So there's two
ways of doing this. You could go number by number
and try to divide 14 into them, or we could just
try to figure out what all of the multiples
of 14 actually are. So let's try to do that. Let's try to do that
second technique. 14 times 1 is 14. You add another 14. 14 times 2 is 28. Add another 14. Let's see, you add 10. You get to 38. Then you add 4 more. You get to 42. Then you add another 14. I haven't seen any of
these numbers show up yet. Add another 14 to this. You get to 56-- still
not quite there. Add another 14. Let's see, if you
add 4, you get to 60, and you have to add the 10. So then you get to 70. And it looks like we have
found one of these numbers. 70 is a multiple of 14. 14 times 1, 2, 3, 4,
5-- 14 times 5 is 70.