Number
FACTORS
The factors of a number are all the numbers that divide into it exactly,
leaving no remainder.
Examples
(a)
Find the factors of 6.
63
62
66
61
=
=
=
=
2
3
1
6
so
so
so
so
3 is a factor
3 is a factor
6 is a factor
1 is a factor
All the factors of 6 are 1, 2, 3 and 6
When we find 2 numbers that multiply together to make another
number, we call them a factor pair.
The factor pairs of 6 are:
(b)
Find the factors of 12 by looking for factor pairs.
12 x 1 = 12
2 x 6 = 12
3 x 4 = 12
(c)
1, 2, 3, 4, 6, 12 are all the factors of 12
Find the factors of 27.
1 x 27 = 27
3 x 9 = 27
(d)
1, 3, 9, 27 are the factors of 27
Find the factors of 25.
1 x 25 = 25
5 x 5 = 25
f lex i p
6x1
and 2 x 3
ac k s
1, 5, 25 are the factors of 25
1
Number
Make sure you understand the examples, then have a go at the
questions below.
A.
By looking for factor pairs, write down all the
factors of the following numbers.
1)
18
2)
24
3)
9
4)
48
5)
30
6)
36
7)
40
8)
14
9)
16
10)
35
Common Factors
The common factors of a set of numbers are factors that are the same.
Examples
(a)
Find the common factors of 6 and 8.
Factors of 6 are
Factors of 8 are
1 2, 3, 6
1 2, 4, 8
1 and 2 are the factors common to both.
The highest common factor (HCF) of 6 and 8 is the highest factor
common to both, so it is 2.
(b)
Find the HCF of 9 and 21.
Factors of 9
Factors of 21
1, 3, 9
1, 3, 7, 21
f lex i p
The HCF is 3
ac k s
2
Number
(c)
Find the HCF of 10, 15, and 25.
Factors of 10 —
15 —
25 —
1, 2, 5, 10
1, 3, 5, 15
1, 5, 25
The HCF is 5.
Make sure you understand the examples.
B.
1)
Find the HCF of each set of numbers.
12 and 16
2)
18 and 27
3) 20 and 30
4)
8 and 12
5) 16 and 24
6)
4, 8 and 12
7) 10, 20 and 25
8)
18, 27 and 36
9) 12, 18 and 30
10)
16, 24 and 40
Using Factors
Example
f lex i p
Write down as many different ways of making 10p with the same type of
coin.
Answer
1,
10p coin
10, 1p
coins
2,
5p coins
5,
2p coins
ac k s
3
Number
C.
Have a go at these questions.
1)
Write down all the ways of making 20p with the same type of
coin.
2)
Write down all the different ways of making 50p with the
same type of coin.
3)
A room has 30 tables to be arranged in rows and columns.
Write down all the different ways this could be done.
4)
Chairs are being set out for a meeting. There are 60 chairs,
to be arranged in rows - what are the different ways it can
be done?
5)
100 cabbage plants are to be planted in rows in a field. Write
down the different ways this can be done.
If the field is square, which is the best way to arrange the
cabbages?
6)
Car parking is to be arranged for a wedding. The cars are to
be parked in rows. 36 cars are expected at the wedding.
Write down the different ways in which the cars could be
parked.
f lex i p
Check your answers, then discuss with your tutor what you need to
work on next.
ac k s
4
Number
Answers
Factors
A
B
C
1) 1, 2, 3, 6, 9, 18
2)
1, 2, 3, 4, 6, 8, 12, 24
3) 1, 3, 9
4)
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
5) 1, 2, 3, 5, 6, 10, 15, 30
6)
1, 2, 3, 4, 6, 9, 12, 18, 36
7) 1, 2, 4, 5, 8, 10, 20, 40
8)
1, 2, 7, 14
9) 1, 2, 4, 8, 16
10)
1, 5, 7, 35
1) 4
2)
9
3) 10
4)
4
5) 8
6)
4
7) 5
8)
9
9) 6
10)
8
1) 1 x 20p coin, 2 x 10p coins, 4 x 5p coins, 10 x 2p coins, 20 x 1p
coins.
2) 50 x 1p coins, 25 x 2p coins, 10 x 5p coins, 5 x 10p coins, 1 x 50p
coin.
3) 1 row of 30 tables, 2 rows of 15, 3 rows of 10, 5 rows of 6.
4) 1 row of 60, 2 rows of 30, 3 rows of 20, 4 rows of 15, 5 rows of 12,
6 rows of 10.
5) 1 row of 100, 2 rows of 50, 4 rows of 25, 5 rows of 20, 10
of 10.
rows
f lex i p
6) 1 row of 36, 2 rows of 18, 3 rows of 12, 4 rows of 9, 6 rows of 6.
ac k s
5