Hello and welcome to Maths with Jay
Here we want to write 8400 as a product of prime factors, so let's start by
writing down prime numbers: the first few primes are
2, 3, 5, 7 and nine isn't prime because three threes are nine, so the next one is 11 and
then we've got 13, so that should be enough for this example.
So what we're aiming to do is to write 8400 as a product of some of these numbers. So
that means we're looking to write it as two times three times... and so on but we
may find that there's more than one two, more than one 3, and so on, but we can start
off by just writing 8400 as a product of two numbers. And you can start off with
just any two numbers, so one of them doesn't have to be prime; so the easiest
thing to do here, is to say well 8400 is obviously one hundred times 84, so we can
show this in this kind of diagram. And then we can keep going, splitting each
number into two numbers, so we're going to have a look at a hundred and write that
as something times something, so we could maybe use ten times ten, that's one
possibility so a hundred is ten times ten, and then similarly looking at
eighty-four: one possibility is 12 times seven
and this time we've actually hit upon one of our prime numbers, so that means that
can't be broken down any further: seven can only be written as one times seven;
there are no other factors of seven other than one and seven, so let's put a
circle round the 7 to indicate that we've got one of our prime numbers and that
isn't going to break down any further. So going back to 10: well ten can be written
as two times five; and both of those numbers are prime, so let's put circles
round those, and the same sort of thing for the other 10.
And then twelve: well one way of factorizing 12 would be to say that it's
three times 4. 3 is prime so let's circle that. And 4: well that can be written as two
times two, and two is prime.
So now we've done all of the hard work, and all we need to do now is write down
the answer: so 8400 is equal to the product of all the circled numbers; so
however you factorise 8400 - you might have started off by saying it was two
times 4200 - however you started off, you would have ended up with the same answer.
So let's write down the answer in an organized kind of way, so we'll start with
all the 2s first of all, so 8400 is two times two times two times two - so that's all
the 2s dealt with. Then there's just one 3, so times 3, two 5s, so that's times five times five, and
finally times seven. So that's a bit long winded. Instead of writing out all those
2s and both of the 5s like that, we could just use index notation.
So we can simply write 8400 is 2 to the power of four times three times five
squared times seven; and you could key that into a calculator to check it.Or you may like
to have a go at using a calculator to work out the answer in the first place.
So what we need to do is key in the number eight thousand four hundred, and
we need to input the number, so we're going to press the equals key and the key that will do
the factorising for us has got the word or part of the word factorise on
it: it's got the word FACT on it in yellow, so we use the Shift key and then
the FACT button and then we get the same answer as before.