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: 2^{3} × 3^{2} × 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.
You have now completed Unit 2 Section 2
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