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Tests of Divisibility of Numbers

Divisibility test is a test which helps us to know whether a whole number is completely divisible
by another number or not. Let’s learn about the tests of divisibility of some numbers.

Divisibility Divisibility Test Example
by

2 A number is divisible by 2 if it is an even 43,602 is divisible by 2 since the digit
number, i.e., the digit at its ones place at its ones place is 2, which is an even
is 0, 2, 4, 6 or 8. number.
3 A number is divisible by 3 if the sum of 408 is divisible by 3 since the sum of
its digits is divisible by 3. its digits, i.e., 4 + 0 + 8 is 12, which is
divisible by 3.

4 A number is divisible by 4 if the number 2,448 is divisible by 4 since the number
formed by its last two digits (i.e., ones formed by its last two digits is 48, which
and tens) is divisible by 4. is divisible by 4.
5 A number is divisible by 5 if the digit at 42,565 is divisible by 5 since the digit at
its ones place is either 0 or 5. its ones place is 5.

6 A number is divisible by 6 if it is divisible 6,324 is divisible by 6 since the number
by both 2 and 3. is divisible by both 2 and 3.
8 A number is divisible by 8 if the number 2,816 is divisible by 8 since the number
formed by the last three digits is either formed by its last three digits is divisible
0 or a number that is exactly divisible by 8, i.e., 816  8 = 102.
by 8.

9 A number is divisible by 9 if the sum of 13,005 is divisible by 9 since the sum of
its digits is divisible by 9. its digits, i.e., 1 + 3 + 0 + 0 + 5 is 9, which
is divisible by 9.
10 A number is divisible by 10 if the digit 7,83,420 is divisible by 10 since the digit
at its ones place is 0. at its ones place is 0.

11 A number is divisible by 11 if the 85,437 is divisible by 11 since the sum
difference between the sum of the of the digits at the odd places, i.e.,
digits at odd places and the sum of the 8 + 4 + 7 is 19 and the sum of the digit
digits at even places is either 0 or a at the even places, i.e., 5 + 3 is 8. The
number that is divisible by 11. difference between 19 and 8 is 11, so
the number is divisible by 11.

Example 10: Check the divisibility of 70,965 by 3 and 9.
Solution: Sum of all the digits of 70,965
Mental Maths
7 + 0 + 9 + 6 + 5 = 27 Is (4,090 + 3180 – 2,000) divisible

27 is divisible by both 3 and 9. So, 70,965 by 2, 5 and 10?
is also divisible by both 3 and 9.

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