Download product of primes

WJEC MATHEMATICS
INTERMEDIATE
NUMBER
PRODUCT OF PRIMES
1
Contents
Decoding the Question
Prime Factor Tree
Index form
Perfect Square
LCM and HCF from Prime Factor Trees
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
2
Decoding the Question
The wording of the question is complex, so let's decode it!
"Write 360 as a product of its prime factors in index form"
A string of
multiply signs
The 'circled'
numbers on the
prime factor tree
Written using
power (indices)
notation
Prime Factor Tree
Creating a prime factor tree using one key skill - splitting a number in
to a factor pair. (Which means, find two numbers that multiply
together to give a certain number.)
Examples
240
240
24
10
12
240
20
60
4
Here, you can see three ways of 'splitting' 240. When creating a
prime factor tree it does not matter which you chose.
To create a prime factor tree, begin with the number in the
question and continue splitting as much as you can.
When you see a prime number - CIRCLE IT
If there's a number that's not circled, then split it!
3
Example
Write 360 as a product of its prime factors
Complete the 'Number
360
Properties' booklet to
learn about Prime
6
2
10
36
Numbers
6
3
5
2
2
3
You could split your numbers in a different way, your answer will be
the same!
The above tree tells you that 360 = 2×2×2×3×3×5
Index form
Make sure that you turn your answer into index form. See 'Powers
and Roots' for more help with this.
360 = 2×2×2×3×3×5
23
32
360 = 23 ×32 ×5
4
Exercise N35
Write the following numbers as a product of its prime factors in index
form:
a. 180
d. 50
g. 256
b. 60
e. 198
h. 500
c. 396
f. 735
i. 7
Perfect Square
For a number to be a perfect square the powers must be even
when you write it in index form
Example 1
Remember:
5 = 51
360 = 23 ×32 ×51
Here you can see the powers are not all even. To make the powers
even we need another 2 and another 5.
If we did have another x2 and another x5 we would be multiplying
360 by 2×5 = 10
Example2
5040 = 24 ×32 ×51 ×71
Here you can see the powers are not all even. To make the powers
even we need another 5 and another 7
If we did have another 5 and another 7 we would be multiplying 5040
by 5×7 = 35
Exercise N36
What would you need to multiply the previous Exercise questions
(above) by to make them a perfect square?
5
LCM and HCF using Prime Factor Trees
Make sure you understand Venn Diagrams for this section.
Some questions give you two larger numbers and asks you to
calculate the LCM and HCF of them. In the booklet 'Number
Properties' we learnt how to find the LCM and HCF of smaller
numbers. For this type of question, you need to write both numbers
out as a product of their prime factors (NOT IN INDEX FORM) from
using prime factor trees.
Example
Find the HCF and LCM of 180 and 200
Firstly, use prime factor trees to write both numbers as a product of
their prime factors. For these numbers you get
180 = 2×2×3×3×5
200 = 2×2×2×5×5
We now create a Venn Diagram from these results. Any number in
both lists MEET AS ONE IN THE MIDDLE
180 = 2 x 2 x 3 x 3 x 5
200 = 2 x 2 x 2 x 5 x 5
5
2
Common Mistake!
If there is a two
in both lists
students put two
2's in the middle
2
instead of 1
6
Now, the numbers we have not used go into their respective circle
3
3
5
2
2
5
2
Important!!
• To find the HCF multiply the numbers IN THE CENTRE
SECTION
• To find the LCM multiply ALL THE NUMBERS IN THE VENN
𝐻𝐶𝐹 = 2×2×5 = 20
𝐿𝐶𝑀 = 3×3×2×2×5×2×5 = 1800
Exercise N37
Use the method of Venn Diagrams to find the HCF and LCM of:
a. 100 and 120
d. 140 and 160
b. 200 and 300
e. 280 and 560
c. 80 and 150
f 220 and 330
7
Exam Questions N24
1.
2.
3.
8
4.
5.
9