Welcome to a lesson on factors.
The goals of this video are to determine
the factors of a natural number,
and also to define prime and composite numbers.
First, the natural numbers,
often called the counting numbers,
is the set of numbers that we see listed here,
one, two, three, four, five, and so on.
Factors are the numbers that divide evenly
into a given number.
This means a factor divides into another number
and there is no remainder.
So for example, if we let N be a natural number,
and X times Y is equal to N,
then X and Y are both factors of the number N.
Quick example of this would be the factors of 15
are one, three, five, and 15,
since one times 15 is equal to 15,
and three times five is equal to 15.
So to find the factors of a number,
it's often easiest to make a list of the two numbers
that multiply to give us the given number.
So to find the factors of 24,
we'll list each pair of numbers
that, when multiplied, give us 24.
So for example, one times 24 is equal to 24,
so these are both factors of 24.
Two times 12 is equal to 24,
three times eight is equal to 24,
and so is four times six.
All of these would be the factors of 24.
Now this is a work that helps us find the factors,
we still need to list them.
And we'll list them from least to greatest.
So we'll have one, two, three, four, and then
six, eight, 12, 24.
Now let's do the same for 54,
we want to find two numbers that multiply together
to give us 54.
And of course, the most obvious one would be one times 54.
It's even, so we could have two times what, 27?
It's also divisible by three,
we can obtain 54 by multiplying three and 18.
And then lastly, we have six times nine.
So all of these would be factors of 54.
And again, we'll list them in order from least to greatest,
so we have one, two, three, six,
nine, 18, 27, and 54.
These are all the numbers that divide evenly into 54.
Let's go ahead and try a couple more.
Here we have 120.
Now of course, as this number gets larger,
it gets more and more challenging
to find all of the factors.
So we need to be sure we take our time here.
We have one times 120.
It's even, so that would be two times 60.
It is divisible by three, that would be three times 40.
It's also divisible by four,
so that would be four times 30.
It ends in a zero, so it's divisible by five.
It should be five times 24.
It's also divisible by six, that would be six times 20.
It's also divisible by eight, we could obtain 120
from the product of eight and 15.
And then lastly, we can also obtain 120
by multiplying 10 and 12.
So these are all the factors of 120.
So let's go ahead and list them,
we have one, two, three, four,
five, six, eight, ten,
12, 15, 20, 24,
30, 40, 60, and 120.
Okay, let's go ahead and take a look at one more.
We have the number 23.
Of course, we can obtain 23 by multiplying one times itself.
Now there aren't any other numbers
that we can multiply together to get 23.
So 23 only has two factors.
One, and itself.
And because this number only has two factors,
it has a special name, it's called a prime number.
So let's go ahead and finish
by talking about prime and composite numbers.
A prime number is a natural number, greater than one,
that has only two factors: one and itself.
And here's a list of the first several prime numbers.
And of course, now we can add 23 to this list,
because we just found that 23 only had two factors as well.
All of the other examples were
what's called a composite number.
A composite number is a natural number
that has more than two factors.
So going back to our examples,
this is the only number here that had two factors,
120, 54, and 24 all had more than two factors,
and therefore, are called composite numbers.
And a special note, the number one is neither prime
or composite by definition.
Okay, hope you found this video helpful,
thank you for watching.