Test of Divisibility

The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not.

Test of divisibility by 2:

A number is divisible by 2, if its units digit is even, i.e., if its units digit is any of the digits 0, 2, 4, 6 or 8.

For a number in the generalized form:

(i) A general two-digit number 10a + b is divisible by 2 if ’b’ is any of the digits 0, 2, 4, 6 or 8.

(ii) A general three-digit number 100a + 10b + c is divisible by 2 if ’c’ is any of the digits 0, 2, 4, 6 or 8.

For example, each of the numbers 54, 42, 62, 70, 88, 96, 342, 406, 964, 730, etc., is divisible by 2.

Test of divisibility by 3:

A number is divisible by 3, if the sum of its digits is divisible by 3.

For a number in the generalized form:

(1) A general two-digit number 10a + b is divisible by 3 if (a + b) is divisible by 3.

(ii) A general three-digit number 100a + 10b + c is divisible by 3 if (a + b + c) is divisible by 3.

For example, each of the numbers 42, 12, 24, 36, 123, 456, 789, 972, etc., is divisible by 3. Also, each of the numbers 71, 53, 94, 26, 134, 361, 985, etc., is not divisible by 3.


Test of divisibility by 5:

A number is divisible by 5, if its unit’s digit is either 0 or 5.

For a number in the generalized form:

(i) A general two-digit number 10a + b is divisible by 5 if ‘b’ is either 0 or 5.

(ii) A general three-digit number 100a + 10b + c is divisible by 5 if ‘c’ is either 0 or 5.

For example, each of the numbers 65, 70, 35, 15, 90, 340, 265, 805, etc., is divisible by 5.


Test of divisibility by 9:

A number is divisible by 9, if the sum of its digits is divisible by 9.

For a number in the generalized form:

(i) A general two-digit number 10a + b is divisible by 9 if (a + b) is divisible by 9.

(ii) A general three-digit number 100a + 10b + c is divisible by 9 if

(a + b + c) is divisible by 9.

For example, each of the numbers 45, 63, 72, 18, 324, 459, 792, 387, etc., is divisible by 9.


Test of divisibility by 10:

A number is divisible by 10, if its unit’s digit is 0.

For a number in the generalized form:

(i) A general two-digit number 10a + b is divisible by 10, if ‘b’ is equal to 0.

(ii) A general three-digit number 100a + 10b + c is divisible by 10 if ‘c’ is equal to 0.

For example, each of the numbers 20, 70, 40, 10, 300, 530, 690, 180, etc., is divisible by 10.


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