Page 1 - 16.2 CH-16-LESSON NOTE(DIVISIBILITY)

SAI International School
Grade -VIII

Mathematics
Chapter- 14: PLAYING WITH NUMBER

SUB TOPIC: DIVISIBILITY

Lesson Note:

Tests of Divisiblity:
(i) Divisibility by 2: A number is divisible by 2 when its one’s digit is 0, 2,
4, 6 or 8.Explanation: Given number abc = 100a +10b +c. 100a and 10b
are divisible by 2 because 100 and 10 are divisible by 2. Thus given
number is divisible by 2 only when a = 0, 2, 4, 6 or 8.
(ii) Divisibility by 3: A number is divisible by 3 when the sum of its digits
is divisible by 3. Example: given number = 61785. Sum of digits =
6+1+7+8+5 = 27 which is divisible by 3. Therefore, 61785 is divisible y 3.
(iii) Divisibility by 4: A number is divisible by 4 when the number formed
by its last two digits is divisible by 4.
Example: 6216, 548, etc.
(iv) Divisibility by 5: A number is divisible by 5 when its ones digit is 0 or
5.
Example: 645, 540 etc.
(v) Divisibility by 6: A number is divisible by 6 when it is divisible by both
2 and 3.
Example: 246, 7230, etc.
(vi) Divisibility by 9: A number is divisible by 9 when the sum of its digits
is divisible by 9.
Example: consider a number 215847. Sum of digits = 2+1+5+8+4+7 = 27
which is divisible by 9. Therefore, 215847 is divisible by 9.
(vii) Divisibility by 10: A number is divisible by 10 when its ones digit is 0.
Example: 540, 890, etc.
(viii) Divisibility by 11: A number is divisible by 11 when the difference of
the sum of its digits in odd places and the sum of its digits in even places
is either o or a multiple of 11.
Example: consider a number 462.
Sum of digits in odd places = 4+2 = 6
Sum of digits in even places = 6
Difference = 6-6=0, which is zero. So, the number is divisible by 11.

Example- 1

1. If 21y5 is a multiple of 9, where y is a digit, what is the value of y?