okay factoring is the fundamental idea
taking number heart into smaller numbers
whose factors when multiplied together equal numbers that we started with
so let's take a look at that and until March grass
the idea and will have the number 12
now 12 is in a very large numbers but you can still be broken apart
smaller numbers so when we're looking for the factors
12 we're also asking the question were different
ways arriving the number 12 and one way it is
to have 6 times to we also have
three times for 12 times
1 and we also have two times two times
3 so there are many different ways of writing the number 12
and fact the only for the same number
with important thing to note
fears that we call each of these factors
and specifically they are factors of the number 12
so this is the notion a factory
next I want to point out something very important that involves this lhasa
here and looking at this lhasa
we can see that the contains small those factors 12
because they cannot be divided on any further
and because they cannot be laid down any further
we actually have a special name and mathematics for them
we call them crime numbers
nope
and by definition prime numbers are whole numbers
that are larger than 1 so that's why we only include the number one
because the whole numbers larger than 1 which includes homely
to factors which are you 1
times itself so too is a prime number
because it contains only two factors which are one
times itself which is to three is also prime number
because contains just only two factors
which are one-timed itself
which three now
six is not a prime number because it contains more than two factors which are
into
times three and six times one so
because it's not a prime number we did in fact call that the composite number
and composite numbers our numbers are contained within two factors
so tall as an example composite number because it contains
more than two factors which are
123 456 factors
so this is the year
notion of prime positive numbers
okay so I want to do now is colourless the
first few prime numbers that we have and because the prime numbers of whole
numbers
that is larger than 1 and contains only two factors
will start with the number two so
to use one of her first prime numbers next we have
30 Ford is not a prime number
because it has more than two factors so
next we have fine 7
6 89 hand are composite numbers which means you have more than two factors
sore neck summers 11 13
17
19 and the list continues
on now there's no exact pattern
find although crime numbers that exist but knowing the first few days
sufficient enough to help us with factory on
so what I want to do now
is show you an easy way factoring numbers
and will start with the example
number 36 and
the method I'm gonna show you scold entry method which stars
with our number and up to my room will control two branches
and at the end two branches
we're going to try and think a to factors other number 36
and they can be into factors that you can think of
so there are many possibilities now looking at the number 36 I nor is it is
an
even number which means I can divide by the number two
and that leaves me with
18 on the other side when I have more
when I moved hi AT&T together I know with more reverts back to the number 36
so now looking at these two numbers
I know isn't who is on my list prime numbers
which means I cannot break down any further
an all-star with number two 18
is a composite number which means I can break down further
so I'm gonna Jo another sub treaty
and think I'll
to factors %uh number eighteen
and I can put here and the one that comes to mind
are to and nine now again
to know who is a prime number as I can see here and i also
remember from to any team so I can start with number two
nine is a composite number which means I can break down
further and all drawn another tree
and again think two factors
and one that comes to mind are 3
and 3 now looking at number three I know is it is on my list
prime numbers which means it cannot be broken down you
further and I will stop number three
now looking at this
overall structure you can see how the numbers are connected together
three in 3d this mean I'm 9 to kiss me 18
18 to reverse the back to 36
which is number that I started with so that
tree method connects these numbers together and as you can see on the
bottom
we are left with all prime numbers
so what we did has a special name
called crime
factorization
and with prime factorization is take a new number
factoring it down to its crime
number components as you can see here
we are left with to 23 3 and
what we can do is writing talent more
playing together and what we are left with the answer is
number that we start with which is 36%
so you can see how
prime numbers are very important factoring
pin number okay with
when I'm gonna do now is we're gonna factor
larger number that's a little bit more challenging and
one china number 1000 again we'll start with our number
and using the tree matter who control two branches
and we're going to try to think two factors of number one thousand
we can think of and for me
when it comes to mind are 10
and a hundred because when you want to cry a hundred times 10
no call back to the number one thousand okay first we'll look at the number ten
and we're gonna try to think two factors
and when it comes to mind cartoon
fine now looking at 2&5 I noticed it is on my list
prime numbers which means it cannot be broken down
further so I'll stop there and now I'm left with number one hundred
and I'm gonna try to think two factors among the 100 I can't think I'll
and one comes to mind art and
10 now
I remember 10 from my previous
number that I as factor and I us remember that the contains
two factors 2&5 so I can go ahead and
easily right down factors and I also remember that two and five are
on my list prime numbers which means they cannot be
the right down to me further an all-star
there so as you can see
we the prime factorization the number one thousand
and we are left with its prime
number components when we write it down we're left with two
2x2 tires lifetimes time times
fine and the result he calls from the minute we started with