How_To_Be_Good_At_Math

NUMBERS • PRIME FACTORS 35

Different tree, same answer

There are often lots of ways to make a factor tree. Here’s

another tree for 72, starting by dividing it by 2. Can you finish

it? There’s more than one way – as long as you get the same

list of prime factors as in Step 4, you’ve done it correctly!

TRY IT OUT

Answer on page 319

Factor trees

An easy way to find the prime factors of a number

is to draw a diagram called a factor tree.

Now when we factor the 4, we get

2 and 2. Both are prime numbers

so we circle them, too.

Let’s find the prime factors of 72. We know from

our multiplication tables that 8 and 9 are factors

of 72, so we can write the information like this.

Now let’s go back to the 9. It can’t be divided

by 2, but it can be divided by 3, giving two

factors of 3. Both are prime numbers, so now we

can write all the prime factors of 72 like this:

72 = 2 × 2 × 2 × 3 × 3

2

72

8

4

2 2

9

2 3 3

72

8

4

2 2

9

2

72

8

4

(^729)
8 9
Neither 8 or 9 are prime numbers, so we
need to break them down some more.
When we factor 8, we get 2 and 4. We put a
circle round 2, because it’s a prime number.
The factors of each
number are written
below it
We stop
looking for
factors when
we find a
prime number
Start by
finding two
factors
of 36
72
2 36
??
034_035_Prime_Factors.indd 35 29/02/2016 14:08