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# Divisibility tests for 2, 3, 4, 5, 6, 9, 10

## Video transcript

what we're going to do in this video are some real quick tests to see if these three random numbers are divisible by any of these numbers here and I'm not going to focus a lot on the why of why they're divisible we'll do that in other videos but really just to give you a sense of how do you actually test to see if this is divisible by 2 or 5 or 9 or 10 so let's get started so to test whether any of these are divisible by 2 you really just have to look at the ones place and see if the ones place is divisible by 2 and right over here 8 is divisible by 2 so this thing is going to be divisible by 2 0 is considered to be divisible by 2 so this is going to be divisible by 2 another way to think about it is if you have an even number over here and 0 is considered to be an even number then you're going to be divisible by 2 so and over here you do not have a number that is divisible by 2 this is not an even number this 5 so this is not divisible by 2 so I won't write any 2 there so we've gone through the twos now let's work through the threes so the to figure out if you're divisible by 3 you really just have to add up all the digits and figure out if the sum is divisible by 3 so let's do that so if I do 2 plus 7 plus 9 actually let me we could let me just write it out plus 9 plus 5 plus 8 plus 8 what's this going to be equal to 2 plus 7 is 9 9 plus 9 is 18 plus 9 is 27 plus 5 is 32 plus 8 is 40 plus 8 is 48 and 48 is divisible by 3 but in case you're not sure so this is equal to 48 in case you're not sure whether it's divisible by 3 you can just add these digits up again so 4 plus 8 is equal to 12 and 12 clearly is divisible by 3 and if you're not even sure there you could add those two digits up 1 plus 2 is equal to 3 and so this is divisible by 3 this right over here let's add up the digits so we can do this one in our head pretty easily 5 plus 6 is 11 11 plus 7 is 18 18 plus 0 is 18 and if you want to add the 1 plus 8 on the 18 you get 9 so the digits add up to 9 digits let me do this enough so these add up to nine add well they add to 18 which if you which is clearly divisible by 3 n by 9 and these two things will add to 9 so the important thing to know is when you add up all the digits the sum is divisible by 3 so this is divisible by 3 as well divisible by 3 and then finally let's add up these digits 1 plus 0 plus 0 plus 7 is 8 plus 6 is 14 plus 5 is 19 that is 8 yet for 19 so that we summed up the digits 19 is not divisible by 3 so this one we're not going to write a 3 right over there it's not divisible by 3 let's try 4 and to think about 4 you just have to look at the last two digits and to see are the last two digits divisible are the last two digits divisible by 4 immediately you can look at this one right over here see it's an odd number if it's not going to be divisible by 2 it's definitely not going to be divisible by 4 so this one this one's not divisible by any of these first four numbers all these first few numbers right over here let's think about this 188 is that divisible by 4 and you could do that in your head that's 4 times 22 so this is divisible by 4 now let's see 4 goes into 60 15 times and then to go from 60 to 70 you have to another 10 which is not divisible by 4 so that's not divisible by 4 and you could even try to divide it out yourself 4 goes into 70 C 1 times you subtract you get a 30 four goes into 30 seven times you multiply then you subtract you get a two right over here as your remainder so it is not divisible by 4 now let's move on to now let's move on to 5 and this is probably you're probably already very familiar with this if your final digit is a 5 or a 0 you are divisible by 5 so this one is not divisible by 5 this one is divisible by 5 you have a 0 there so this is divisible by 5 and this you have a 5 as your ones digit so once again finally this is divisible by something it's divisible by five now the number six the simple way to think about divisible divisibility by six is that you have to be divisible by both 2 and 3 in order to be divisible by 6 because the prime factorization of 6 is 2 times 3 so here we're divisible by 2 and 3 so we're going to be divisible by we do that in a new color so we're going to be divisible by 6 here we're divisible by 2 and 3 so we're going to be divisible by 6 and if you're just divisible by 2 or 3 just one of them then you wouldn't be able to do this you have to have both a 2 and a 3 divisibility by both of them and here you're divisible by neither 2 or 2 nor 3 so you're not going to be divisible by 6 now let's do the test for 9 the test for 9 is very similar to the test for 3 sum up all the digits if that sum is divisible by 9 then you're there well we already summed up the digits here 48 48 actually is not divisible by 9 if you're not sure you can add up the digits there you get 12 12 is definitely not divisible by 9 so this thing right over here is not divisible by 9 and this one over here if you added up all the dish we got 18 which is divisible it is divisible by 9 and I'm running out of colors so this one is divisible by 9 they're all the digits add it up to 18 and this one over here you don't even have to add them up because we already know it's not divisible by 3 if it's not divisible by 3 can't be divisible by 8 but if you did add up the digits you get 19 which is not divisible by 9 so this also is not divisible by 9 and then finally divisibility by 10 and this is the easiest one of all because you just have to see if you have a 0 in the ones place you clearly do not have a 0 in the ones place here you do have a 0 in the ones place there so you are divisible by 10 here and then finally you don't have a 0 in the ones place here so you're not going to be divisible by 10 another way you could think about it you have to be divisible by both 2 and 5 to be divisible by 10 here that your you are divisible by 5 but not by 2 but obviously the easiest one is to just see if you have a 0 in the ones place