Finding factors and multiples | Factors and multiples | Pre-Algebra | Khan Academy


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.

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