The why of the 3 divisibility rule | Factors and multiples | Pre-Algebra | Khan Academy

Why you can add the digits to see if something is divisible by 3

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[lelosaiyan]

I hate it when strangers run up to me with questions about the divisibility of 3.

[BigSadClownBoi]

Sometimes I watch these videos just to hear him talk. I remember the days many years ago when these saved me in math classes.

[Kram]

multiples of 3 where you know it's divisible by any other numbers it consists of, for instance, if the last digit is even and the digit sum is divisible by 3, the whole thing is divisible by 6. If the sum is 9, 18 divides it, if the last digit is 5, 15 or 45 divide it respectively or if the last digit is 0, 1, 2, 3, 5, 6, 10, 30 or, if its sum is 9, 90 and 9 divide it.
Generalizing the other way: It works for any factor of base-1
In base 61, it works for all things that divide 60.

[jesseweneedtocook]

2 + 2 is 4...
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.
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MInUS OnE ThaT'S ThreEE QuiCK MaFfS

[RiyadhElalami]

I have been thinking about this for the last 15 years (I am 18)
I have always known this but never understood why and never searched for it but now you are my man.

[raydredX]

You have two numbers a and b. Both divisible by 3, therefore:
a=3n
b=3m
Therefore:
a+b=3n+3m=3(n+m)
Therefore (a+b) is divisible by 3.

(n and m are just some random natural numbers.)

[vtvtify]

Also works for checking divisibility by 9

[albertroswell]

thank you, nice video!, someday i'll make a spanish version, thank you

[sophiah]

THANK YOU SO MUCH you just make it more ez!

[VishnuAi]

These last few Videos are amazing, This is Why i never got Elementary arithmetic. They Never explained it, or told us WHY things works, just little tricks and tips that would fade from memory.

[thuytran-xfwz]

I am learning a lot from your web site Khan.

[thelir]

I know this is simple but still... how can someone come up with this? This is the most random thing a human can think about
Liked by the way

[aka]

that's because of the presence of '1' inside the brackets, which in turn is used to represent hundred or ten as 1 plus 99or1 plus9, since all numbers can be written in terms of sums of different place values and since the place values are always represented as multiples of 100 or 10 or higher, we can always write them as 1 plus 9999(any number of 9's accordingly).This is all because ours is a BASE 10 system, all these tests wont be true for other base systems.

[Kram]

he actually uploaded the divisibility by 9 video just before he uploaded a video on divisibility by 3, saying exactly what you just did. Yes, that works.

[peachy]

i really thank you for this tutorial this is something that I've have always have trouble with. until i found this video. God Bless!

[nctyodream]

thank you so much it helped me for my exam review!

[sookoonator]

I did not know about adding the numbers and if it is a multiple of 3 it can be divided by 3 thing but now I know it and why it is like that in one

[raydredX]

I was never taught this kind of stuff in school very deeply. But I started doing Olympiads maths for fun and this kind of thinking shows up a lot. Do you know where I can learn more about it?

[kldhmd]

hi khan,
thanks for this helpful videos but
can you teach us about Lagrangian?

and thanks again.

[grayswandir]

I remember this proof from a number theory class in college back in the late seventies. In the class we used a(1+99) + b(1+9) etc.