Page 149 - Ganit Kaushal

Divisibility by 10

A number is divisible by 10 if the digit at the ones place is 0. For example: 80 is divisible by 10 because the
digit at its ones place is 0.

5.7 SOME MORE DIVISIBILITY RULES

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.
For example: 276 is divisible by 3, since the sum of its digits, 2 + 7 + 6 = 15, and 15 is divisible by 3.

Divisibility by 6

6 is a multiple of both 2 and 3. The rule for divisibility by 6 is a combination of the rules of divisibility for 2
and 3. So, a number is divisible by 6 if it is even and if the sum of its digits is divisible by 3. For example:
42 is even and the sum of its digits, 4 + 2 = 6, is divisible by 3, so it is divisible by 6. Similarly, 78, 114, 120,
132, 144, etc. are divisible by 6.

Divisibility by 7

A number is divisible by 7 if the difference between the sums of numbers in alternate blocks of three digits
from right to left is divisible by 7.

For example:
(i) Consider the number 47532911272.
The sum of the numbers in alternate blocks [shown by blue and red colours] of three digits from
right to left is 272 + 532 = 804 and 911 + 47 = 958.

Their difference = 958 – 804 = 154, which is divisible by 7.
\ The given number 47532911272 is divisible by 7.
(ii) Consider the number 6805793192.
The sum of the numbers in alternate blocks [shown by blue and red colours] of three digits from
right to left is 192 + 805 = 997 and 793 + 6 = 799.

Their difference = 997 – 799 = 198, which is not divisible by 7.
\ The given number 6805793192 is not divisible by 7.

Divisibility by 9

A number is divisible by 9 if the sum of the digits of the number is divisible by 9.
For example: The number 5481 is divisible by 9, since the sum of its digits, 5 + 4 + 8 + 1 = 18, and 18 is
divisible by 9. Similarly, 639, 729, 8514, and 5886 are divisible by 9.

Divisibility by 11

A number is divisible by 11 if the difference between the sum of its digits in the odd positions and the sum of
its digits in the even positions is either 0 or divisible by 11.

Prime Time 147