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# Finding factors of a number

CCSS.Math:

## Video transcript

find all of the factors of 120 or another way to think about it find all of the whole numbers that are that 120 is divisible by so the first one that's maybe obvious all whole numbers are divisible by one so we could write 120 it is equal to it is equal to one times 120 so let's write a factors list over here factors factors right here so this is going to be our factors list over here so we just found two factors we said well is it divisible by one well every whole number is divisible by one this is a whole number so one is a factor at the low end one is a factor that's it's actually low its smallest factor its largest factor is 120 you can't have something you can't have something larger than 120 dividing evenly into 120 hunt you know 121 will not go into 120 so the largest factor on our factors list is going to be 120 now let's think about others let's think about whether is 2 divisible into 120 so does 120 equal 2 times something well when you look here you immediately or maybe you immediately recognize that 120 is an even number it's ones place is a 0 as long as it's ones place is a 0 2 4 6 or 8 as long as it's an even number where the whole number is even and the whole number is divisible by 2 and to figure out what you have to multiply by 2 to get 120 well you could think of well 120 is is is 12 times 10 or another way to think about it it's 2 times 6 times 10 or 2 times 60 you could divide it out if you want you could say okay 2 goes into 120 2 goes into 1 no times 2 goes into 12 6 times 6 times 2 is 12 subtract you get 0 bring down the 0 2 goes into 0 0 times 0 times 2 is 0 and you get no remainder there so it goes 60 times so we have two more factors right here so we have the factors so we've established so the next lowest one is 2 and the next highest factor if we're storing from the large end is going to be 60 is 60 now let's think about what the three is 120 is 120 equal to three times something well we could just try to test and divide it from the get-go but you hopefully already know the divisibility rule to figure out if something is divisible by three you add up its digits and if the sum is divisible by three we're in business so if you take 120 so that you're dealing with so this is one let me do it over here one plus two plus zero well that's equal to one plus two is three plus zero is three and three is definitely divisible by three so this is 120 is going to be divisible by three and to figure what that number that you have to multiply by three is you could do it in your head you could say well 3 goes into 12 four times and then you well let me just do it out just in case just for those of you who want to see it worked out 3 goes into 12 4 times 4 times 3 is 12 you subtract you're left with nothing here you bring down this 0 3 toes into 0 0 times 0 times 3 is 0 nothing left over so it goes into it 40 times 40 times and the way to think of it in your head is this is the same thing as 12 times 10 12 divided by 3 is 4 but this is going to be 4 times 10 because you have that 10 left over whatever works for you or you can just ignore the 0 divided by 3 you get a 4 and then put the zero back there whatever works so we have two more factors at the low end we have a 3 and at the high end we have a 40 we have a 40 now let's see if 4 is divisible into 120 now we saw the divisibility rule for 4 is you ignore everything beyond the tens place and you just look at the last two digits so if we're going to if we're going to think about the whether 4 is divisible you just look at the last two digits the last two digits are 20 20 is definitely divisible by 4 so 120 will be divisible by 4 4 is going to be a factor and to figure out what we have to multiply 4 by to get 120 you could do it in your head you could say 12 divided by 4 is 3 so 120 divided by 4 is 30 so we have two more factors four and thirty and you could work this out long division if you if you want to make sure that this works out so let's keep going and then we have we'll see what the 120 is equal to is five a factor is five times something equal to 120 well you can't do that simple well first of all we could just test is it divisible and 120 ends with a 0 if you end with a 0 or 5 you are divisible by 5 so 5 definitely goes into it and let's figure out how many times so 5 goes into 120 doesn't go into 1 it goes into 12 2 times 2 times 5 is 10 subtract you get to bring down the 0 5 goes into 20 4 times 4 times 5 is 20 and then you subtract and then you subtract and you have no leftover as we expect because it should go in evenly this number ends with a 0 or 5 so 5 let me delete all this so we can have our scratch space to work with later on so 5 times 24 is also equal to 120 so we have 2 more factors 5 and 24 and let me clear up some space here because I think we're going to be dealing with a lot of factors so let me move this right here so let me cut it and then let me paste it move this over here so we have more space for our factors so we have 5 and 24 let's move on to 6 so 120 is equal to 6 times what now did it be divisible by 6 you have to be divisible by 2 and 3 now we know that we're already divisible by 2 and 3 so we're definitely going to be divisible by 6 and you should hopefully be able to do this one in your head 5 was a little bit harder to do in your head but 120 you could say well 12 divided by 6 is 2 and then you have that 0 there so 120 divided by 6 would be 20 and you could work it out long division if you like so 6 times 20 are 2 more factors 6 times 20 now let's think about 7 let's think about 7 here 7 is a very bizarre number and just to test it you could think of other ways to do it let's just try to divide 7 into 127 doesn't go into 1 it goes into 12 one time 1 times 7 is 7 you subtract 12 minus 7 is 5 bring down the 0 7 goes into 57 times 7 is 49 so it goes into it 7 times 7 times 7 is 49 subtract you have a remainder so it does not divide evenly so 7 does not work 7 does not work now let's think about 8 let's think about whether 8 works let's think about 8 I'll do the same process let's take 8 into 120 and just as a little bit well let's just let's just see let's just work it out and just as a little bit of a hint well I'll just work it out 8 goes into 12 it doesn't go into 1 so it goes into 12 one time 1 times 8 is 8 subtract there 12 minus 8 is 4 bring down the 0 8 goes into 40 5 times 5 times 8 is 40 and you're left with no remainder so it goes evenly so 120 let me get rid of that 120 120 is equal to 8 times 15 so let's put add that to our factor list we now have an 8 and now we have a and now we have a 15 now is it divisible by 9 is 120 divisible by 9 to test that out you just add up the digits 1 plus 2 plus 0 is equal to 3 well that satisfies our three divisibility rule but 3 is not divisible by 9 so our number will not be divisible by 9 so 9 will not work out 9 does not work out so let's move on to 10 well this is pretty straightforward it ends in 0 so we will be divisible by 10 so let me write that down 120 is equal to 10 times and this is pretty straightforward 10 times 12 you could this is exactly what 120 is it's 10 times 12 so let's write those factors down and twelve and then we have one number left we have eleven we don't have to go above eleven because we already went through twelve and we know that there aren't any factors above that because we did we these are we were going in descending order so we've really filled in all the gaps and you could try eleven we could try it by hand if you like 11 goes into 120 now you know if you know your multiplication tables through 11 that this won't work but I'll just show you 11 goes into 12 one time 1 times 11 is 11 subtract 1 bring down the 0 11 goes into 10 0 times 0 times 11 is 0 you're left with a remainder of 10 so 11 goes into 20 10 times with the remainder 10 definitely does not go in evenly so we have all of our factors here 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 and 120 and we're done