Write 48 as a product of its prime
There are three things we really
need to pay attention to when answering this question. The first is the word
“product.” When we find the product of two
numbers, we multiply them. Let’s bear this in mind at the
end. The second is this word
“prime.” A prime number is a number which
has exactly two factors: one and itself.
The first five prime numbers are
two, three, five, seven, and 11. It’s important we remember that one
is not a prime number. One actually only has one factor
since it can be divided by one and itself, itself being one.
And we have to start showing the
word “factor.” But let’s remind ourselves what
that means. It’s a number that divides evenly
into another number, without leaving a remainder. Now, when we write 48 as a product
of its prime factors, we tend to use something called a factor tree.
To find the first two numbers in
our factor tree, we need to find two numbers that multiplied together to make
48. Ideally, one of these will be
prime, but this isn’t entirely necessary. 48 is an even number. That means it can be divided by
two. When we divide 48 by two, we get
24. We said that two was a prime
number. So we’re going to stop here. We can draw a circle around the
number two to show that we’ve finished on this branch.
24 is not a prime number. So we need to find two numbers that
again multiplied to make 24. Since 24 is even though, we know it
can be divided by two. And when we divide 24 by two, we
get 12. Since this two is also a prime
number, we put a circle around this. And we finished on this branch.
12 isn’t. So let’s find two numbers that
multiply to make 12. 12 is even. So two is a nice, easy number to
choose. When we divide 12 by two, we get
six. And once again, we pop a circle
round the number two because it’s prime. And we’re done with this
Let’s repeat this process for the
number six. Six can be divided by two. And when we divide six by two, we
end up with three. Both two and three are prime
numbers. So we draw circles around them both
and we’re done. Remember we said that product means
multiply. So the final step is to multiply
these numbers together.
48 is equal to two multiplied by
two multiplied by two multiplied by two multiplied by three. A common mistake here is to either
separate these numbers with commas or to add them altogether. If we do that, we’re going to be
losing the final mark in this question. We must make sure we write them as
We also don’t need to evaluate;
that’s to find out the answer to two times two times two times two times three
because actually it just gives us 48. And another way to write this will
be two to the power of four multiplied by three. In fact, in this question, that’s
not entirely necessary. But if it had asked us to put it in
index form, that’s what this would have look like.
Now, remember we said that we
didn’t need to find factors of 48 that were prime numbers straightaway. Let’s see what that would have
looked like. Six multiplied by eight is 48. Neither of these are prime
numbers. So I’m not going to circle
them. Six can be written as two
multiplied by three. Since both of these are prime
numbers, we can pop a circle around them.
Eight can be written as two
multiplied by four. And we’ll pop a circle around that
too. And four can be written as two
multiplied by two. Once again, we’ve shown that 48 can
be written as two multiplied by two multiplied by two multiplied by two and
multiplied by three.
In fact, there are a number of
different ways that we can write the factor tree for 48. We will always end up with the same