Common Divisibility Examples

Common Divisibility Examples

In this video I want to do a bunch of
example problems

that show up on standardized exams

and definitely will help you with
our divisibility module

because it's asking questions like this

All numbers, and this is just one of the examples,

All numbers divisible by both 12 and 20
are also divisible by

and the trick here is to realize that if a
number is both divisible by 12 and 20

it has to be divisible by each of
these guy's prime factors

So let's take their prime factorization.

The prime factorization of 12 is 2 time 6

6 isn't prime yet, so 6 is 2 times 3,

So that is prime

so any number divisible by 12 needs to be
divisible by 2 times 2 times 3.

So it's prime factorization needs to have
a 2 times a 2 times a 3 in it

any number that's divisible by 12

Now, any number that's divisible by 20,
needs to be divisible by

Let's take it's prime factorization

2 times 10, 10 is 2 times 5

so any number divisible by 20, needs to
also be divisible by 2 times 2 times 5

or another way of thinking about it,

it needs to have two 2's,
and a 5 in it's prime factorization

Now if you're divisible by both, you need
to have two 2's, a 3, and a 5.

two 2's and a 3 for 12,
and then two 2's and a 5 for 20

and you can verify this for yourself
if this is divisible by both

Obviously, if you divide it by 20, is the same
thing as dividing it by 2 times 2 times 5

So you're going to have,

the 2's are going to cancel out,
the 5's are going to cancel out

your just going to have a 3 leftover,
so it's clearly divisible by 20

and if you were to divide it by 12,
you'd divide it by 2 times 2 times 3

this is the same thing as 12

and so these guys would cancel out,
and you would just have a 5 leftover

so it's clearly divisible by both,
and this number right here is 60

it's 4 times 3, which is 12,
times 5. It's 60

This right here is actually
the least common multiple of 12 and 20