Divisibility Tests Or Divisibility Rules

By Manjit Singh Atwal
Divisibility Tests For Math Kids

Kids in grade six or higher grades should be able to tell quickly if a number is divisible by small prime numbers, such as 2, 3 or 5. Divisibility test or rules are very helpful to predict the divisibility of large numbers. I have explained the basic tests one by one in this presentation.

1. Divisibility test for 2:

All the numbers having one of the digits from 0, 2, 4, 6, 8 at their ones place are divisible by 2. For example; numbers 338, 5334, 924, 10002 and 23440 have the ones digit as 8, 4, 4, 2 and 0 respectively, hence are divisible by 2. On the other hand, 23669 has 9 at ones place, hence not divisible by 2.

2. Test for 3:

To test the divisibility for three, add all the digits of the number and if the sum is divisible by three then the given number is also divisible by three. If the sum is not divisible by three then the given number is not divisible by 3 as well. For example; given number is 61224, and we want to check if this number is divisible by 3. To test add all the digits of the number (6 + 1+ 2 + 2 + 4 =15), the sum of digits is 15 and which is divisible by 3, hence 61224 is divisible by 3. In other words it can be said that 3 is a factor of 61224.

3. Test for 4:

If the number formed using the tens and ones digits of the given number is divisible by 4 then the given number is divisible by 4. For example; consider the given number is 916 and the tens and ones digits make 16 which can be divided by 4, hence 916 is divisible by 4.

4. Test for 5:

If the ones digit is "0" or "5" then the number can be divided by 5. For example; consider the given number is 30085, as the ones digit is 5, hence the given number 30085, can be divided by 5.

5. Test for 6:

If a given number is divisible by 2 and 3 both then it can be divided by 6 too. For example; consider the given number is 774. This number is divisible by 2, as the ones digit is four. Now add the digits (7 + 7 + 4 = 15) to get 15 and which is divisible by 3, hence 774 is divisible by 3 too. Now because 774 is divisible by 2 and 3 both therefore it is divisible by 6 as well.

6. Test for 9:

Test for 9 is similar to test for 3. Add all the digits of the number and if the sum can be divided by 9 then the number itself can be divided by 9.

7. Test for 10:

If the ones digit of a number is zero then this number can be divided by 10. For example; 230 has "0" at ones place, hence it is divisible by 10.

Keep in mind that if a given number is divisible by 2 then 2 is called the factor of the given number.

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