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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 and 8
so we don't have to worry about those. So let's think about 2. So are we divisible by 2? Let me write the 2 here. 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 digit-- so let me rewrite 380. To be even, your ones digit
has to be even, so 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 for 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, so it's just 11. And if you have trouble figuring
out whether this is divisible by 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 1 or the 2, neither of these are divisible by 3. So not divisible by 3, and 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 380 is not divisible. 380, not divisible by 3,
so 3 does not work. We are not divisible by 3. Now, I'll think about the
situation for 4, so we're thinking about 4 divisibility. So let me write it in orange. So we are wondering about 4. 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 leftover, whether
the 80, is divisible by 4. Another way to think about it
is are the last two digits divisible by 4? And this comes from the fact
that 100 is divisible by 4, so everything, the hundreds place
or above, it's going to be divisible by 4. You just have to worry
about the last part. So in this situation, is
80 divisible by 4? Now, you could eyeball that. You could say, well, 8 is
definitely divisible by 4. 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. So let's do 5. I'll actually scroll
down a little bit. Let's try 5. So what's the pattern when
something is divisible by 5? Let's do the multiple of 5? 5, 10, 15, 20, 25. So if something's divisible by
5-- I could keep going-- 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. 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 are divisible by 2 and you are
divisible by 3. If you're divisible by both
2 and 3, you'll 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. So divisibility by 9. So you can make a similar
argument here that if something is not divisible by
3, there's no way it's going to be divisible by 9 because
9 is equal to 3 times 3. So to be divisible by 9, you
have to be divisible by 3 at least twice. At least two 3's have to go
into your number, and this isn't the case, so you could
already knock 9 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 divisibility by 3. We can add the digits. So you add 3 plus 8 plus
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 whether
it's divisible by 9. So lastly, we have
the number 10. We have the number 10, and
this is on 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 does end with zero, or its
ones 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 and 9.