Multiples, Factors and Primes MTH 3- 05a,b
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Multiples
A multiple of a number is a number that appears in the extended times table of that
number.
For example, multiples of 6 would be 6, 12, 18, 24, 30, …………….
Lowest Common Multiple (LCM)
This is the smallest number that is divisible by a pair of numbers.
Example: Find the LCM of 8 and 12
Multiples of 8:
8, 16, 24, 32, 40, 48, 64, 72 ……..
Multiples of 12:
12, 24, 36, 48, 60, 72……….
Common multiples are numbers that appear in both lists: 24, 48, 72, ….
The lowest of these is 24 so the LCM = 24.
Exercise:

1.
State the first 5 multiples of: a) 3
b) 7
2.
State the multiples of 9 which lie between 30 and 70.
3.
State the multiples of 12 which lie between 40 and 100.
4.
Find the lowest common multiple of:
a) 4 and 5
b) 6 and 9
c) 12 and 16
c) 11
d) 3, 5 and 6
Factors
A factor of a number is a number that divides into that number exactly.
For example, factors of 16 are 1, 2, 4, 8, 16.
It is a good idea to look for pairs of factors so that all factors are found.
For example, find all of the factors of 36:
1 x 36
2 x 18
3 x 12
4x9
6x6
So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Highest Common Factor
The highest common factor of a pair of numbers is the largest value that will fit into both
numbers.
Example: Find the highest common factor of 24 and 30.
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Factors of 30:
1, 2, 3, 5, 6, 10, 15, 30
Common factors are numbers that appear in both lists: 1, 2, 3, 6
The highest of these is 6 so HCF = 6.
Exercise:
1.
Find all of the factors of these numbers:
a) 18
2.
b) 20
d) 50
e) 100
f) 72
Find the highest common factor of:
a) 4 and 10

c) 32
b) 18 and 30
c) 21 and 35
d) 48 and 60
Prime Numbers
Prime numbers are numbers with exactly 2 factors. i.e. they only divide by 1 and
themselves.
Note that : 1 is not a prime number (it has only one factor)
2 is the only even prime number.
The sequence of prime numbers starts: 2, 3, 5, 7, 11, 13, 17, …..
Exercise:
1. Write down the next 5 prime numbers.
2. Which of these numbers is prime?
1,
9,
21,
23,
37,
39,
49,
65,
87,
121