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42 Maths

TESTS FOR DIVISIBILITY OF NUMBERS
By using the actual division, we check whether a given number is divisible by another. If the remainder is zero,
we conclude it is exactly divisible by the second number. However, there are some divisibility tests which help
us come to a conclusion about the divisibility of a given number by any of the numbers 2, 3, 4, 5, 6, 8, 9, 10 and
11 without actually carrying out the long division. We have already studied about the divisibility tests in Class V.
Let’s review these tests here again.

Divisibility by 2
A number is divisible by 2, only if its last digit (ones place digit) is either 0 or divisible by 2.
For example; 22, 24, 46, 136, 404, 435130 are all divisible by 2.

Divisibility by 3
A number is divisible by 3, only if the sum of its digits is divisible by 3.
For example; 3450 is divisible by 3, as 3 + 4 + 5 + 0 = 12 which is divisible by 3.

Divisibility by 4
A number is divisible by 4, only if the number formed by its last two digits is divisible by 4 or if the number ends
in two zeros.
For example; 824, 6036, 100, 79852 are all divisible by 4.

Divisibility by 5
A number is divisible by 5, only if its ones digit is either 0 or 5.
For example; 25, 210, 4905, 3170 are all divisible by 5.

Divisibility by 6
A number is divisible by 6, only if it is divisible by both 2 and 3.
For example, 750, 5922, 2070, 2518302 all are divisible by 6.

Divisibility by 8
A number is divisible by 8, only if the number formed by its last three digits is divisible by 8 or if the number
ends in three zeros.

For example; 1000, 989464, 1016, 63840 are all divisible by 8.
Divisibility by 9

A number is divisible by 9, only if the sum of its digits is divisible by 9.
For example; 9801 = 9 + 8 + 0 + 1= 18, which is divisible by 9. Hence, 9801 is divisible by 9.
Also, 666 = 6 + 6 + 6 = 18, which is divisible by 9. Hence, 666 is divisible by 9.

Divisibility by 10
A number is divisible by 10, only if its ones digit is 0.
For example; 20, 90, 1000, 1250, 15440 are all divisible by 10.

Divisibility by 11

A number is divisible by 11, if the difference of the sums of its alternate digits is either 0 or divisible by 11.
For example; 7931 is divisible by 11 as (7 + 3) – (9 + 1) = 0.
Also, 9635604 is divisible by 11 as (9 + 3 + 6 + 4) – (6 + 5 + 0) = 11 is divisible by 11.