This document explains how to write numbers as the product of their prime factors. It provides examples of decomposing the numbers 36 and 28 into their prime factors. To find the prime factors of a number, you think of two numbers that multiply to the given number. If those numbers are prime, they are the prime factors. If not, you continue decomposing the non-prime numbers into more prime factors until only prime numbers remain. For example, 36 decomposes to 2 x 2 x 3 x 3 = 22 x 32 and 28 decomposes to 2 x 2 x 7 = 22 x 7.

1. Objective
Be able to write a number as the
product of prime factors

2. Remember the prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ….
Here are the first ten prime numbers:
Why are they prime?
Each number has only two natural factors.
In every case the two factors are the
number itself and the number 1
The factors
of 2 are 1
and 2
The factors
of 3 are 1
and 3

3. Prime factor decomposition
Write the number 36 as the product of its
prime factors
36
Think of two
numbers
which
multiply
together to
give 36.
We could use
2 and 18
2 18 Now ask
yourself, “are
these prime
numbers?”
Is 2 a prime
number?
Yes. So we
can stop this
part of our
tree here.
Is 18 a prime
number?
No. So we
carry on
2
2
9
3 3
2
3 3
36 = 2 x 2 x 3 x 3
36 = 22
x 32

4. Prime factor decomposition
Write the number 28 as the product of its
prime factors
28
Think of two
numbers
which
multiply
together to
give 28.
We could use
7 and 4
7 4
Now ask
yourself, “are
these prime
numbers?”
Is 7 a prime
number?
Yes. So we
can stop this
part of our
tree here.
Is 4 a prime
number?No. So we
carry on
2
7
2
2
28 = 2 x 2 x 7
28 = 22
x 7
2

5. Now try some interactive questions
Click here to begin

6. Objective
Be able to write a number as the
product of prime factors

7. Objective
Be able to write a number as the
product of prime factors