# Unit 2 Section 2 : Prime Factors

A factor tree can be used to help find the prime factors of a number.

The tree is constructed for a particular number by looking for pairs of values which multiply together to give that number.
These pairs are added as "leaves" below the original number. If a leaf is prime, then it can be circled as it is a prime factor.
Leaves which are not prime can be broken down in the same way as the original number, until all the leaves are prime.

The slideshow below shows how to find the prime factors of 36 using a factor tree.

Breaking 36 into its prime factors using a factor tree.

Of course, we didn't necessarily need to start by breaking 36 into 9 and 4.
The next slideshow shows what happens if you break the 36 into 6 and 6.

Breaking 36 into its prime factors using a "different" factor tree.

A factor tree for the number 36 will always give "2", "2", "3" and "3" as the prime factors.
The number 36 can be written as a product of its prime factors by multiplying these four numbers together.

Writing 36 as a product of its prime factors gives 2 × 2 × 3 × 3

## Example Question 1

For each of the numbers below, draw factor trees on paper to write the number as a product of its prime factors.
Work out the answer then click on the button marked to see whether you are correct.

The answers can be written in any order, but we tend to put the smallest prime factors first.

(a) Write 102 as a product of its prime factors

(b) Write 60 as a product of its prime factors

## Example Question 2

A number is expressed as a product of its prime factors as:     23 × 32 × 5

What is the number

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Below are three incomplete factor trees.
Fill in the gaps in each one then use the button to see if you are correct.
(a)

(b)

(c)

Question 2
Below are three incomplete factor trees for the number 66.
Complete the factor trees in three different ways.

(a)

(b)

(c)

Question 3
Write each of the numbers below as a product of its prime factors.
You may find it helpful to draw a factor tree on paper for each one.
You will need to use the asterisk (*) as a multiply sign.

For example, the answer for the number 30 would look like this:

 (a) 62 (b) 64 (c) 82 (d) 320 (e) 90 (f) 120 (g) 54 (h) 38 (i) 1000

Question 4
A number is expressed as a product of its prime factors as: 2³ × 3 × 5²
What is the number?

Question 5
A particular number has prime factors 2, 3 and 7.
What are the 3 smallest values the number could be? (separate your answers in the box below with commas)

Question 6
What is the smallest number that has:
(a) four different prime factors?
(b) five prime factors?
Question 7
Write down two numbers, neither of which must end in zero (0), and which:
(a) multiply together to give 1000.
The numbers are and
(b) multiply together to give 1000000.
The numbers are and

You have now completed Unit 2 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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