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GRADE : V
SUBJECT: Maths
READING SECTION: 1 Chapter:2 Properties of whole numbers
Prime and composite numbers
Prime numbers:
The natural numbers which are exactly divisible by 1 or by the number itself are called
prime numbers. 2,3,5,7,9,11,13…….etc. are prime numbers.
Composite numbers:
The natural numbers which are exactly divisible by other numbers, along with 1 or itself
are called composite numbers.4,6,8,10,12 etc. are composite numbers.
Note: 1 has only one factor which is itself, so it is neither prime nor composite number
1.Write the numbers 1 to 100 in a table as shown below.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
20 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
a. Circle the number 2 and cross out all other numbers exactly divisible by 2.
b. Circle the number 3 and cross out all other numbers exactly divisible by 3.
c. Circle 5,7 and other remaining numbers which are not crossed and continue the process.
d. Now list the numbers which are circled. What type of numbers are they?
e. Now list the numbers which are crossed out. What type of numbers are they?
Multiples of a number
7 2
7 × 𝟏 = 7 2 × 1 = 2
7 × 2 = 14 2 × 2 = 4
7 × 3 = 21 2 × 3 = 6
7, 14, 21, 28…….. 2, 4, 6 ………. are multiple of 2
are the multiples of 7
Note: Multiples are infinite
Even
numbers
Points to Remember:
1) 1 is a factor of every number
1 x 6 = 6
1 x any number = number itself
any number ÷ 1 = number itself
8 ÷ 1 = 8
2) Every number is a factor of itself.
6 x 1 = 6
any number x 1 = number itself
any number ÷ itself = 1
8 ÷ 8 = 1
3) The factor of a number is always less than or
equal to the number.
Factor of 12: 1, 2, 3, 4, 6 and 12
1 < 12
2 < 12
3 < 12
4 < 12
6 < 12
12= 12
Worked Out Example
a) 36 b) 45 c) 70
36 = 2×2×3×3 45=3×3×5 70= 2×5×7
Note: to get prime factors we will divide by only prime numbers like 2,3,5 ,7 and so on.
Prime Factorisation method
1. Write all the possible factors of these numbers.
a) 15 b) 35 c) 64 d) 18 e) 140
2. Write the first five multiples of these numbers.
a) 5 b) 9 c) 13 d) 16 e) 20
3. Factorize the following numbers using prime factorization process.
a) 14 b) 24 c) 72 d) 100 e) 130
Exercise: 1
HCF and LCM
HCF stands for Highest Common Factor
LCM stands for Lowest Common Multiple
HCF = Product of their common prime
factors
LCM = Product of their common prime
factors and remaining factors
Two methods of finding the HCF
Writing all the possible factors (Method one) Prime factorisation method (Method two)
a) 16, 20
Factors of 16= 1, 2, 4, 8, 16
Factors of 20= 1, 2. 4, 5, 10, 20
Here, common factors= 1, 2, 4
(among these common factors, 4 is the highest)
Therefore H.C.F of 16,20=4
b) 14, 28,42
Factors of 14= 1, 2, 7, 14
Factors of 28= 1, 2, 4, 7, 14, 28
Factors of 42= 1, 2, 3, 6, 7, 14, 21 ,42
Here, common factors = 1, 2, 7, 14
(among these common factors , 14 is the highest)
Therefore H.C.F of 14,28 42= 14
a) 16,20
H.C.F= 2×2
= 4
b) 14, 28, 42
H.C.F= 2×7
=14
1.Write all the possible factors of the following pairs of numbers , circle the common factors
and select the HCF
a) 4 , 6 b) 6, 8 c) 16, 24 d) 18 , 27 e) 5, 10, 15
2.Find the H.C.F of the following pairs of numbers by prime factorisation method.
a) 12, 16 b) 15, 20 c) 24, 30 d) 27, 36 e) 33, 44
f) 12, 18, 24 g) 30, 45, 60
Exercise: 2
Two methods of finding the LCM
Writing the first ten multiples (Method one) Division Process (Method Two)
a) 8, 12
Multiples of 8= 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Multiples of 12= 12, 24, 36, 48, 60, 72, 84, 96 ,108,
120
Here, common multiples are 24, 48 and 72
(among these common multiples 24 is the lowest)
Therefore L.C.M of 8, 12= 24
b) 6, 10, 15
Multiples of 6= 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 10= 10, 20, 30, 40, 50, 60, 70, 80, 90,
100
Multiples of 15= 15, 30, 45, 60, 75, 90, 105, 120, 135,
150
Here common multiples are 30, 60 ( among these
common multiples 30 is the lowest)
Therefore L.C.M of 6, 10, 15 = 30
a) 8, 12
L.C.M = 2 × 2 × 2 × 3
=24
b) 6, 10, 15
L.C.M = 2 × 3 × 5
=30
1.Write the first ten multiples of the following pairs of numbers and select the L.C.M
a) 2, 4 b) 6, 8 c) 7, 14 d) 10 , 20 e) 4, 6, 9
2. Find the L.C.M of the following pairs of numbers by division method.
a) 8, 10 b) 9, 15 c) 16, 24 d) 22, 33
e) 8, 12, 16 f) 18, 24, 36 g) 40, 45, 60
Exercise: 3
READING SECTION: 2 Factorization using factor tree method
i) 18
ii) 32
Exercise: 4
1. Copy and complete the factor tree
2. Express the following numbers as the product of their prime factors using the factor tree
method.
a) 8 b) 27 c) 60 d) 150 e) 200
Here, 32=2 x 16 at first, again
16=2 x 8
Similarly, 8=2 x 4 and 4= 2 x 2.
we will make branch for
composite numbers only and
other numbers are written as
same.
At last, we get only prime
numbers.
