1. Write a number as a product of its prime factors.
HCF and LCM
Objective
Write a number as a product of its prime factors.
Find the highest common factor HCF and lowest common multiple LCM of two numbers
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2. Recap of Prime Numbers To do this work, we use prime numbers
So, here is a recap of these…

3. Prime Numbers - A prime number is a number that can only be divided exactly (no remainder) by itself and 1
No, it can be divided by 2, 4 and 6
Is 12 a prime number?
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 6 = 2
Is 7 a prime number?
Yes, it can only be divided by itself and 1
7 ÷ 7 = 1
7 ÷ 1 = 7

4. Write down the prime numbers between 1 and 40
Notice that 1 is not a prime
It’s a special number called unity 1, 2, 3, 4, 5, 6, 7, 8, 9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39, 40

5. Factors
Factors are the numbers that multiply together to make a certain number.
The factor pairs of 12 are:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
4 x 3 = 12
6 x 2 = 12
12 x 1 = 12

6. We can find prime factors like this…
The prime factors are the prime numbers that multiply together to make a number
The prime factors of 12 are
2 x 2 x 3 = 12
All prime numbers
We can find prime factors like this…

7. How to Find Prime Factors
Find any two factors of 12 12
If prime, stop 2 6
If not prime, find two more factors 3 2
Prime factors of 12 are
2, 2 and 3
Both prime so stop

8. If not prime, find two more factors
An example of how to find the prime factors of 40 40
Find any two factors of 40 10 4
If not prime, find two more factors 2 5
Prime factors of 40 are
2, 2, 2 and 5
All prime stop

9. Find the prime factors of these numbers:1. 20 2.
150 3. 60 4.
210 5.
462 6.
350 7.
390 8.
693

10. Find the prime factors of these numbers:1. 20
2, 2 and 5 2.
150
2, 3, 5 and 5 3. 60
2, 2, 3 and 5 4.
210
2, 3, 5 and 7 5.
462
2, 3, 7 and 11 6.
350
2, 5, 5 and 7 7.
390
2, 3, 5 and 13 8.
693
3, 3, 7 and 11

11. What do we mean by the highest common factor HCF of two numbers?

12. Here is a method for more difficult numbers…
Highest Common Factor (HCF)
This is the largest number that will divide exactly (no remainder) into two numbers.
The HCF of 8 and 12, for example, is 4
It’s easy to see that 4 is the largest number that will divide into both
Here is a method for more difficult numbers…

13. 36 = 2 x 2 x 3 x 3 72 = 2 x 2 x 2 x 3 x 3 2 x 2 x 3 x 3 HCF = HCF = 24
Find the highest common factor (HCF) of 36 and 72
Find the prime factors of both numbers
36 = 2 x 2 x 3 x 3
72 = 2 x 2 x 2 x 3 x 3 2
x 2
x 3
x 3
Use one of each of the numbers that are in both lists like this…
HCF =
HCF = 24

14. Find the highest common factor (HCF) of these pairs of numbers:1.
12 and 30 2.
24 and 156 3.
54 and 180 4.
32 and 104 5.
48 and 144 6.
72 and 168 7.
45 and 75 8.
66 and 110

15. Find the highest common factor (HCF) of these pairs of numbers:1.
12 and 30 6 2.
24 and 156 12 3.
54 and 180 18 4.
32 and 104 8 5.
48 and 144 48 6.
72 and 168 7.
45 and 75 15 8.
66 and 110 22

16. What do we mean by the lowest common multiple LCM of two numbers?

17. Here is a method for more difficult numbers…
Lowest Common Multiple (LCM)
This is the smallest number that is in the times table of both numbers.
The LCM of 9 and 12, for example, is 36
Here is a method for more difficult numbers…
1 x 12 = 12
2 x 12 = 24
3 x 12 = 36
4 x 12 = 48
1 x 9 = 9
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36

18. Find the lowest common multiple (LCM) of 24 and 60
Find the prime factors of both numbers
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5 2
x 2
x 3
Use one of each of the numbers that are in both lists
LCM =
x 2 x 5
And ALL the remaining numbers
LCM = 120

19. Find the lowest common multiple (LCM) of these pairs of numbers:1.
18 and 30 2.
24 and 84 3.
30 and 75 4.
48 and 60 5.
18 and 24 6.
36 and 60 7.
54 and 120 8.
72 and 150

20. Find the lowest common multiple (LCM) of these pairs of numbers:1.
18 and 30 90 2.
24 and 84
168 3.
30 and 75
150 4.
48 and 60
240 5.
18 and 24
360 6.
36 and 60
180 7.
54 and 120
1080 8.
72 and 150
5600