hello and welcome to factoring numbers in this video we're going to talk about
factoring a helpful skill that will prepare you to master algebra and learn
how to work with fractions factorization means that you take a number for example
10 and find all the whole numbers or factors that the number can be divided
by so that the result is still a whole number and not a fraction another way of
saying this is that so the result has no remainder so for example 10 can be
divided by 5 to give us the whole number 2 or it can be divided by 2 to give us
the whole number 5 it can also be divided by 1 to give us the whole number
10 or by 10 to give us the whole number 1 another way of thinking about this is
to say that 2 times 5 is equal to 10 and that 1 times 10 is equal to 10 so now we
know that 1 2 5 and 10 are factors of the whole number or 10 you might notice
something very important one and the number itself are always statues of that
number this means that for any number greater than 1 there are at least two
factors one in itself any number that has only these two factors itself 1 is
called a prime number the prime number is only divisible by 1 and that same
number so for example 2 3 5 7 11 13 17 are some prime numbers and these are
just the first few ones some large numbers can have a lot of factors
finding all of them can take some time but there are some tricks you can learn
that make factoring easier let's take a pretty big number
Say 90 get started you can immediately list two factors like we've discussed
before 1 & 9 all right the first factor one on the
left-hand side of the line in the second factor 90 on the right-hand side of the
line to find more factors start counting up from the bottom so the next number is
290 is an even number therefore it can be divided by two
resulting in 45 so both these numbers are factors we
write to next to one and 45 next comes three and again you'll find that 90 can
be divided by three resulting in 30 so our list of factors now looks like this
then we check for and as it turns out 90 can't be divided by 4 if you don't know
why this is the case please check out some of our learning gains by division
but if you're allowed to use a calculator then it's even easier just
calculate 90 divided by 4 and you'll find the result is 22 point 5 which is
not a whole number
so four is not a factor of 90 but this we've gained a lot of really important
information if four is not a factor then we know that multiples of four such as
eight twelve the sixteen are also not factors of 90 either so keep this in
mind and you won't have to check out these numbers later on then comes five
and I need divided by 5 is equal to 18 so our new list of factors is this 1 2 3
5 in 18 and 90 can also be divided by 6 resulting in 15 so that gives us 1 2 3 5
6 and 15 wow this is already a long list of factors but 98 can't be divided by 7
so 7 and all multiples of southern such as 14 21 won't be added to this list and
we've already excluded 8 because we found that 4 isn't a factor and 8 is a
multiple of 4 next comes 9 and of course 90 divided by 9 is 10 bringing us to 1 2
3 5 6 9 10 15 18 30 45 and 90 and with this we're done we know that we're
finished because the next number we would need to check is 10 and we already
know that this is a factor on the list one cool trick to think about is that if
we reach a number and it's big enough so that the square of that number is bigger
than the number we want to factor we know that we're finished in this example
we've reached 10 10 squared is equal to 100 and 100 is larger than 90 if we were
to keep looking for factors of 90 that are bigger than 10 all we would ever
find are the factors 15 18 30 45 and 90 but these are exactly the same factors
that we have found earlier Congrats you now know all the basic information about
how to factor a number it's basically just trying to find all
the numbers that can divide the original number you were given be sure to
practice your new skills with our fun games and quizzes at always icecream and
clever dragons and I hope to see you soon