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.


 Fun with Numbers

Playing with Numbers

Test of Divisibility

Number Puzzles and Games


 Fun with Numbers - Worksheets

Worksheet on Number Puzzles and Games













8th Grade Math Practice

From Test of Divisibility to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Counting Numbers from 1 to 50 | Match the Number | Missing Numbers

    Apr 04, 25 03:46 PM

    Math Coloring Pages on Counting Number Oredr
    In counting numbers from 1 to 50, recognize the numbers, count and then join the numbers in the correct number order. Here we mainly need eye-hand coordination to draw the picture and maintain the num

    Read More

  2. Counting Eleven to Twenty with Numbers and Words |Numbers from 11 - 20

    Apr 04, 25 03:21 PM

    Counting eleven to twenty with numbers and words are explained below. One ten and one more is eleven. Eleven comes after ten. One ten and two more is twelve. Twelve comes after eleven.

    Read More

  3. 5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers

    Apr 03, 25 03:11 PM

    5th Grade BODMAS Rule Worksheet
    In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying…

    Read More

  4. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 03, 25 02:58 PM

    Worksheet on Simplification
    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  5. Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples

    Apr 03, 25 10:25 AM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More