This document discusses factors, multiples, primes, lowest common multiples (LCM), and highest common factors (HCF). It provides examples and exercises on determining if a number is a multiple, factor, or prime. It also demonstrates how to find the LCM and HCF of two or more numbers, including using Venn diagrams to show the overlapping prime factors. Readers learn to write numbers as a product of prime factors using factor trees.

1. Factors, Multiples, Primes

2. •Use simple tests of divisibility.
•Recognise multiples.
•Recognise primes (less than 100).
•Recognise lowest common multiples.
•Recognise highest common factors.
•Write a number as a product of its prime
factors.
Multiples, Factors and
Primes

3. What are the first five multiples of:
a) 3
b) 4
c) 11
d) 21
3, 6, 9, 12, 15
4, 8, 12, 16, 20
11, 22, 33, 44, 55
21, 42, 63, 84, 105
A multiple of a number is what you get
when you multiply that number by
some other whole number.
Multiples are
Usually
Larger
Than
Individual numbers,
Possibly
Larger never
Ever
Smaller
Factors, Multiples,
Primes

4. • http://www.visnos.com/demos/sieve-of-
eratosthenes
Factors, Multiples,
Primes

5. 7
11 19
23
2
17
3749
9
2245
63 57 81
27
69
77 99
1
X
7 23
17
11 19
X
X 2
X X
X X X
X X X
X X 37
39
Identify the prime numbers in the grid below. There
are 7 to find.
Factors, Multiples,
Primes

6. Lowest Common Multiple – the lowest number
in two or more numbers’ times tables.
Q. Find the LCM of 4 and 6.
1. Write out the first six numbers the 4 and 6
times tables
2. Look for the first number that appears in
both lists.
Factors, Multiples,
Primes.

7. • https://www.youtube.com/watch?v=GKTexzw
Fpck
Factors, Multiples,
Primes

8. Example LCM
Q. Find the LCM of 4 and 6
4  4, 8, 12, 16, 20, 24,….
6  6, 12, 18, 24, 30, 36,…
We want the LOWEST common multiple, so
the LCM of 4 and 6 is… 12
Factors, Multiples,
Primes

9. a) 2 and 5
b) 3 and 4
c) 4 and 8
d) 5 and 6
e) 3 and 8
f) 4 and 9
g) 8 and 10
h) 4, 5 and 12.
10
12
8
30
24
36
40
60
Find the LCM of the following:
Factors, Multiples,
Primes

10. What are the factors of:
a) 16
b) 30
c) 8
d) 7
1, 2, 4, 8, 16
1, 2, 3, 5, 6, 10, 15, 30
1, 2, 4, 8
1, 7
A factor is a whole number which divides
exactly into a whole number, leaving no
remainder.
Factors
Are
Certainly
Tiny
Or
Really
SmallA prime number has exactly two factors:
1, and the number itself.
Factors, Multiples,
Primes

11. • We can use a ‘factor tree’ to enable us to
write a number as “a product of its prime
factors”
• Each time you reach a prime number, you stop
and circle that number.
Factors, Multiples,
Primes

12. • Example: Write 84 as a product of its prime factors
• 84 = 2 x 2 x 3 x 7
• 84 = 22 x 3 x 7
• Now your turn: Write 42 as a product of prime factors.
84
2 42
2 21
3 7
Factors, Multiples,
Primes

13. • Highest Common Factor (HCF) – the
number that goes into two or more numbers
exactly.
• Write out all the factors for each number….
• Example: Find the HCF of 32 and 56
32  1, 2, 4, 8, 16, 32
56  1, 2, 4, 7, 8, 14, 28, 56 HCF = 8
Factors, Multiples,
Primes

14. a) 8 and 12
b) 9 and 15
c) 10 and 30
d) 18 and 33
e) 32 and 80
f) 60 and 108
g) 36, 64, and 76
h) 48, 60 and 84
Find the HCF of the following numbers:
4
3
10
3
16
12
4
12
Factors, Multiples,
Primes

15. Your turn…
1. Find the HCF of the
following:
a) 18 and 28
b) 16 and 40
c) 42 and 90
d) 40 and 63
e) 20, 64 and 108
f) 54, 90 and 162
2. Find the LCM of the
following:
a) 4 and 5
b) 8 and 12
c) 6 and 9
d) 12 and 15
e) 5, 8 and 10
f) 4, 7 and 9
3. Write the following as products of their prime factors.
a) 18 b) 135 c) 154 d) 2310
2
8
6
1
4
18
20
24
18
60
40
252
32 x 2 33 x 5
2 x 7 x 11 2 x 3 x 5 x 7 x 11

16. •Use simple tests of divisibility.
•Recognise multiples.
•Recognise primes (less than 100).
•Recognise lowest common multiples.
•Recognise highest common factors.
•Write a number as a product of its prime
factors.
Factors, Multiples,
Primes

17. HCF and LCM
• Calculate the HCF and LCM of 48 and 60
48 60
48 = 2 x 2 x 2 x 2 x 3

18. 48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
48 60
2
2
2
2
3
3
2 2
5
• Multiply the numbers in the overlap to get the HCF
• Multiply all the numbers in the Venn diagram to get the
LCM.
HCF = 2 x 2 x 3 = 12
LCM = 2 x 2 x 3 x 2 x 2 x 5 = 240
Find the HCF and
LCM of the
following:
24 and 30
36 and 50
16 and 72