1. Factors – factorisation and factor tree
Description
Reflect and Review


Every number
has 1 and itself
as factors.
We can find
factors of a
number by
multiplication
or division
methods.
Teasers

Factors of 37 are 1 and 37, since both 1) Find the
factors
1 and 37 divide 37 without leaving
of 42 by
any remainder, i.e.,
the
1 × 37 = 37 × 1 = 37.To find the
method
factors of 96:
of
multiplic
(a) Using multiplication method
ation
96 = 1 × 96
and
= 2 × 48
division.
= 3 × 32
2) Draw
= 4 × 24
the
= 6 × 16
factor
= 8 × 12
tree of
Therefore, the factors of 96 are 1, 2, 3, 4,
56.
6, 8, 12, 16, 24, 32, 48 and 96.
Answers
1) 1, 2, 3, 6, 7,
14, 21 and 42
2)
56
2
28
2
14
2
7
(b) Using division method
96 ÷ 1= 96
96 ÷ 2= 48
96 ÷ 3= 32
96 ÷ 4= 24
96 ÷ 6= 16
96 ÷ 8= 12
Therefore, the factors of 96 are 1, 2, 3, 4,
6, 8, 12, 16, 24, 32, 48 and 96.


A factor tree
gives
information
about all the
factors of a
number except
1.
Factor tree of 96 is
96
2
2
48
96
24
2
12
2
6
2
3
1
2. Common factors and HCF
Description


A number is said to be a
common factor of two or more
numbers if it is a factor of each
of the given numbers.
HCF (Highest Common Factor) of
two or more numbers is the
greatest common factor of the
given numbers.
Reflect and Review
Teasers
To determine the common
factors and hence the HCF of
48 and 72:
1) Find the
HCF of 28
and 35.
2) Find the
HCF of 24
and 15.
48 = 1 × 48
= 2 × 24
= 3 × 16
= 4 × 12
=6×8
The factors of 48 are 1, 2, 3,
4, 6, 8, 12, 16, 24 and 48
Answers
1) 7
2) 3
72 = 1 × 72
= 2 × 36
= 3 × 24
= 4 × 18
= 6 × 12
=8×9
The factors of 72 are 1, 2, 3,
4, 6, 8, 9, 12, 18, 24, 36 and
72.
Common factors of 48 and 72
are 1, 2, 3, 4, 6, 8, 12 and 24.
Out of these, 24 is the
greatest.
Thus, 24 is the HCF of 48 and
72.
3. Prime and Composite numbers; Even and Odd numbers
Description
Reflect and
Teasers
Review

2
Numbers which have only two

11, 13, 17, 19, 23
1) The number
Answers
1) 2


factors, 1 and itself, are called
Prime numbers, whereas all
other numbers which have
more than two factors are called
Composite numbers.

1 is neither prime nor
composite, as it has only one
factor, which is itself.
A number which leaves 0 as
remainder when divided by 2 is
Even number and which leaves
1 as remainder is Odd number.
4. Multiples
Description




The multiples of a number are
found by multiplying it with any
counting number.
Every number is a multiple of
itself.
A number is said to be a common
multiple of two or more numbers
if it is a multiple of each of the
given numbers.
LCM (Least Common Multiple) of
two or more numbers is the
smallest common multiple of the
given numbers.
and 29 are the
prime numbers
between 10 and
30.
1 = 1 × 1, so 1 has
only one factor.2,
4, 6, 8, ....., 20 are
ten even numbers
from 1 to 20.
1, 3, 5, 7, ….., 19
are ten odd
numbers from 1 to
20.
which is even
and also
prime is
______.
2) Write a
number
which is odd
and also
composite.
______
3) Write a
number
which is even
and also
composite.
______
4) Write a
number
which is odd
and also
prime.
______
Reflect and
Review
Teasers
To determine the
common multiples and
hence the LCM of 12
and 15:
1) Find the first 3
common
multiples of 3
and 4.
2) Find the LCM
of 24 and 32.
Multiples of 12: 12, 24,
36, 48, 60, 72, 84….
2) 9
3) 12
4) 7
Answers
1) 12, 24
and 36
2) 96
Multiples of 15: 15, 30,
45, 60, 75, 90, 105….
Out of these, 60 is the
smallest.
Thus, the LCM of 12
and 15 is 60.
3
5. Divisibility rules of 2, 5 and 10.
Description
Reflect and Review
A number is divisible by
another number if the
second number is a
factor of the first
number, or we can say
that a number is
divisible by another
number if division of
the first number by the
second leaves no
remainder. Following
are the Divisibility Rules
of 2, 5 and 10:



4
Divisibility by 2:
A number is
divisible by 2 if the
digit at the ones
place of the
number is 0, 2, 4, 6
or 8.
Divisibility by 5:
A number is
divisible by 5 if the
digit at the ones
place of the
number is 0 or 5.
Divisibility by 10:
A number is
divisible by 10 if the
digit at the ones
place of the
number is 0.
Check the divisibility with 2, 5 or 10 for
the following numbers:
35, 67, 40, 56, 108, 28, 69, 110.




Numbers divisible by 2:
40, 56, 108, 28, 110 …since the last
digit of each of these is either 0, 2,
4, 6, 8 or 0.
Numbers divisible by 5:
35, 40, 110 …since the last digit of
each of these is either 0 or 5.
Numbers divisible by 10:
40, 110 …since the last digit of
each of these is 0.
Numbers not divisible by 2, 5 or
10: 67, 69 …since none of the
divisibility rules are fulfilled.
Teasers
Answers
1) Find
which of
the
following
numbers
are
divisible
by 2, 5
and 10.
345, 239, 340,
4006, 231,
325, 1014,
4000
Divisible by 2:
340, 4006,
1014, 4000
Divisible by 5:
345, 340, 325,
4000
Divisible by
10: 340, 4000