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# Recognizing divisibility

## Video transcript

determine whether 380 is divisible by 2 3 4 5 6 9 or 10 they skipped 7 & 8 so we don't have to worry about those so let's think about 2 so let's think about so are we divisible by 2 let me write the 2 here divisible by 2 well in order for something to be divisible by 2 it has to be an even number and to be an even number your ones digits so let me read that rewrite 380 to be even your ones digit has to be even so then this has to be even and for this to be even it has to be 0 2 4 6 or 8 and this is 0 so 380 is even which means it is divisible by 2 so it works with 2 so 2 works out let's think about the situation 4 3 now a quick way to think about 3 so let me write just 3 question mark is to add the digits of your number and if the sum that you get is divisible by 3 then you are divisible by 3 so let's try to do that so 380 let's add the digits 3 plus 8 plus 0 is equal to 3 plus 8 is 11 plus 0 is so it's just 11 and if you have trouble with figuring out with a dissident like 3 you could then just add these two numbers again so you can actually add the 1 plus 1 again and you would get a 2 regardless of whether you look at the 11 or the 2 neither of these are divisible by 3 so not not divisible visible 5/3 maybe in a future video I'll explain why this works and maybe you want to think about why this works so these aren't divisible by 3 so three hundred eighty so three hundred and eighty is not divisible 380 not not divisible by three so three does not work we are not divisible by three now let's think about the situation let's think about the situation for 4 so if we're thinking about 4 divisibility so let me write it in orange so we are wondering about for now something you may or may not already realize is that 100 is divisible by 4 it goes evenly so this is 380 so the 300 is divisible by 4 so we just have to figure out whether the left over whether the 80 is divisible by 4 another way to think about it is are the last two digits last two digits divisible by 4 and this comes from the fact that 100 is divisible by 4 so everything on the hundreds place were above it's going to be the life or you just have to worry about the last part so in this situation is 80 divisible by 4 now you could I ball that you could say well 8 is definitely divisible by 4 or 80 divided by 8 divided by 4 is 2 80 divided by 4 is 20 so this works yes yes so since 80 is divisible by 4 380 is also divisible by 4 so 4 works for work so let's do 5 make sure you scroll down a little bit let's try 5 so what's the pattern when something is divisible by 5 let's do the multiples of 5 5 10 15 20 25 so if something is divisible by 5 I could keep going so divisible by 5 that means it ends with either a 5 or a 0 right every multiple of 5 either has a 5 or a 0 in the ones place so 5 or 0 in ones place ones place now 380 has a 0 in the ones place so it is divisible by 5 now let's think about the situation for 6 let's think about what happens with 6 so we want to know are we divisible by 6 so to be divisible by 6 you have to be divisible by the things that make up 6 remember 6 is equal to 2 times 3 so if you're divisible by 6 that means you're divisible by - and you are divisible by three if you're divisible by both 2 and 3 you will be divisible by 6 now 380 is divisible by 2 but we've already established that it is not divisible by 3 if it's not divisible by 3 it cannot be divisible by 6 so this gets knocked out we are not divisible by 6 now let's go to 9 let's go to 9 so divisibility by 9 so you can make a similar argument here that if if something is not divisible by 3 there's no way it's going to be divisible by 9 because 9 9 is equal to 3 times 3 so to be divisible by 9 you have to be divisible by it by 3 at least twice at least two threes have to go into your number and this isn't the case so you could already knock nine out but if we didn't already know that we're not divisible by 3 the other way to do it is a very similar way to figure out divisible by divisibility by 3 and we can add the digits so you add 3 + 8 + 0 and you get 11 and you say is this divisible by 9 and you say this is not divisible by 9 so 380 must not be divisible by 9 and for 3 you do the same thing but you test whether the sum is divisible by 3 for 9 you test with a certain is 1 by 9 so last Li we have the number 10 we have the number 10 and this is in some level the easiest one what do all the multiples of 10 look like 10 20 30 40 we could just keep going on and on they all end with zero or if something ends with zero it is divisible by 10 380 is the visit does end with zero or it's once place does have a zero on it so it is divisible by 10 so we're divisible by all of these numbers except for 3 6 & 9