The test of divisibility by a number ‘x’ is a shortcut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not.
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 twodigit number 10a + b is divisible by 2 if ’b’ is any of the digits 0, 2, 4, 6 or 8.
(ii) A general threedigit 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.
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 twodigit number 10a + b is divisible by 3 if (a + b) is divisible by 3.
(ii) A general threedigit 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.
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 twodigit number 10a + b is divisible by 5 if ‘b’ is either 0 or 5.
(ii) A general threedigit 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.
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 twodigit number 10a + b is divisible by 9 if (a + b) is divisible by 9.
(ii) A general threedigit 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.
A number is divisible by 10, if its unit’s digit is 0.
For a number in the generalized form:
(i) A general twodigit number 10a + b is divisible by 10, if ‘b’ is equal to 0.
(ii) A general threedigit 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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