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.