FACTOR AND MULTIPLES
FACTORS
Factors are numbers that divide exactly into
another number.
The factors of 12, for example, are 1, 2, 3, 4, 6
and 12.
=> 12 / 2 = 6 with no remainder, then 12 /6 = 2.
Thus, factors are in pairs and the pairs multiply to be the factors of the number
The factors of 12 are:
1 x 12 = 12 => 1 and 12 are factors of 12.
2 x 6 = 12 => 2 and 6 are factors for 12
3 x 4 = 12 => 3 and 4 are factors for 12.
The factors of 12 are 1, 2, 3, 4, 6 and 12.
All numbers greater than 1 has at least 2 factors :-
1 and the number itself
2 = 1 x 2. 1 and 2 are factors of 2
3 = 1 x 3. 1 and 3 are factors of 3
4 = 1 x 4 and 2 x 2. 1, 2 and 4 are
factors of 4.
Example:
Find all the factors of 20.
Method
Step 1: List out the 2 factors of 1 and the number itself
20
= 1 x 20
Step2: Multiply from 2 until numbers
2
x 10 = 20,
3 –
no
4
x 5 = 20
6,7,8,9
– no.
10
found in 2 x 10. – can stop trying.
Step3: Answer
The factors of 20 are 1, 2, 4, 5, 10 and 20
Example:
Find all the factors of 36.
Method
Step 1: List out the 2 factors of 1 and the number itself
36
= 1 x 36
Step2: Multiply from 2 until ‘repeated’
factor
2
x 18 = 36,
3 x
12 = 36
4
x 9 – 36
5 –
no
6
x 6 = 36
7,8
– no.
9
found in 4 x 9 (repeated) can stop trying.
Step3: Answer
The
factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Common
Factors
Factors
of 6 : Factors
of 9 :
1 x 6 1 x 9
2
x 3 3 x 3
1 and 3
are common factors of 6 and 9.
Example:
Find the common factors of 24 and 36.
Method
Step1: List out the factors of both numbers
24 = 1 x 24 36 = 1 x 36
= 2 x 12 = 2
x 18
=
3 x 8 = 3 x 12
=
4 x 6 = 4 x 9
= 6 x 6
Step2: Circle/Underline the common factors
24 = 1
x 24 36 = 1 x 36
= 2 x 12 = 2
x 18
=
3 x 8 = 3 x 12
=
4 x 6 = 4
x 9
= 6
x 6
Step3: Solve
The
common factors are 1, 2, 3, 4, 6 and 12
MULTIPLES
Multiples are
extended times tables
The multiples
of 2 are all the
numbers in the 2 times table:
2, 4, 6, 8, 10, ...
Multiples of 2 always end with a 2, 4, 6, 8 or 0.
2, 4, 6, 8, 10, ...
Multiples of 2 always end with a 2, 4, 6, 8 or 0.
Example:
2478 is a multiple of 2 because it
ends with 8.
The multiples
of 5 are all the
numbers in the 5 times table:
5, 10, 15, 20, 25, ...
Multiples of 5 always end with a 5 or 0.
5, 10, 15, 20, 25, ...
Multiples of 5 always end with a 5 or 0.
Example:
395 is a multiple of 5 because it ends
with a 5.
The multiples
of 10 are all the
numbers in the 10 times table:
10, 20, 30, 40, 50, …
Multiples of 10 always end with a 0.
10, 20, 30, 40, 50, …
Multiples of 10 always end with a 0.
Example:
9910
is a multiple of 10 because it ends with a 0.
Common Multiple
First
5 multiples of 4: 4,8,12,16,20
First
5 multiples of 5: 5,10, 15, 20, 25
20
is a multiple of both 4 and 5.
=>
20 is a common multiple of 4 and 5.
