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CCSS.Math:

which of the following numbers is a factor of 154 so 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 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 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 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 5 times 5 times 3 is 15 subtract then we 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 a 5 or a 0 in the ones place you see that if we're 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 a 5 or a 0 in 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 can make the same argument for 9 if something is divisible by 9 its 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 as 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 150 for 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 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 14 times 1 is 14 you add another 14 14 times 2 is 28 add another 14 let's see 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 256 still not quite there at another 14 let's see if you had 4 you get to 60 and then you have to add the 10 so then you get 270 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