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CHAPTER FACTORS AND MULTIPLES
Aim
The aim of this lesson is to solve problems involving
factors and multiples.
objective
At the end of this lesson, students will be able to
understand and solve problems involving
 Factors
 Prime factors
 Highest common factor H.C.F
 Multiples
 Least common multiple L.C.M
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Factors and multiples
Factors
Defn.
Whole numbers which multiply to give a certain
number are called the factors of that number.
Ex 1.
Factors of 24 are 1 , 24
2 , 12 ,
3 , 8 ,
4 , 6 ,
Ex 2.
Factors of 36 are 1 , 36
2 , 18 ,
3 , 12 ,
4 , 9 ,
6 ,
Ex 3. Evaluation
Find the factors of 8 , 12 , 9 , 20 and 84
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Factors and multiples
Prime numbers
Defn.
Prime numbers are numbers which have exactly two
factors, namely 1 and the number itself.
Note :
1 is not a prime number because it has only one
factor, i.e 1 itself.
e.g 2 , 3, 5, 7 , 11 , 13 , 17 , 19 , ….
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12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 6 = 2
12 can be divided by 2,
4 and 6 so 12 is not a
prime number.
7 ÷ 7 = 1
7 ÷ 1 = 7
7 can only be divided
by itself and 1 to
give an integer
answer. 7 is a prime
number
Prime numbers
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Copy the table below and circle the prime
numbers between 1 and 40.
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
Ex
Soln.
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
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Prime factors
Defn.
Prime factors are those factors of a number
which are prime numbers.
30 = 2 × 3 × 5
24 = 2 × 2 × 2 × 3
= 23 × 3 Index notation
60 = 2 × 2 × 3 × 5
= 22 × 3 × 5 Index notation
30
2
15
3
5
5
1
24
2
12
2
6
2
3
3
1

Ex. Find the prime factorisation of
(a) 30 (b) 24 (c) 60
(a)
(b)
(c)
Soln.

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Highest Common Factor H.C.F
H.C.F
Defn.
The H.C.F of two or more numbers is the largest
common factor among the common factors of the
numbers.
Ex 1. Find the H.C.F of 12 and 18.
Soln.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
H.C.F = 2 × 3
= 6
Select
common
factors
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Highest Common Factor H.C.F
Ex 2. Find the H.C.F of 24 , 32 , 36.
Soln.
24 = 2 × 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
H.C.F = 2 × 2
= 4
36 = 2 × 2 × 3 × 3
Step 2. Select
factors
common to 24,
32 and 36

Step 1. Find the prime factorisation of
24, 32 and 36 .

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Multiples
Multiples of 2 are 2 , 4 , 6 , 8 , 10 , 12 , ………
Multiples of 3 are 3 , 6 , 9 , 12 , 15 , 18 , ……..
Ex 1.
Ex 2.
Evaluation
List the multiples of 4.
List the multiples of 5.
Ex 3.
Ex 4.
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Least Common Multiple L.C.M
L.C.M
Defn.
The L.C.M of two or more numbers is the smallest
common multiple of the numbers.
Ex 1. Find the L.C.M of 12 and 18.
Soln.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
L.C.M = 2 × 2 × 3 × 3
= 36

Find the prime factorisation of 12 and 18.