# Maths : Divisibility Tests for 2 to 11

Here are the basic divisibility tests that might be useful :

**2** – Check whether the unit place of the number is even. (i.e) 2,4,6,8.

**3** – Check whether the sum of the digits is divisible by 3.

**4** – Check whether the number formed by the last two digits of the number is divisible by 4.

**5** – Check whether the last digit (unit place) is either 5 or 0.

**6** – Check whether the number satisfies the divisibility tests for 2 and 3.

**8** – Check whether the number formed by the last 3 digits is divisible by 8

**9** – Check whether the sum of the digits is divisible by 9.

**11** – Difference of the sum of the odd places and sum of the even places of the number should be ‘0’ or divisible by 11.

**Divisibilty Test for 7 :**

Test #1. Take the digits of the number in reverse order, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary. Add the products. This sum has the same remainder mod 7 as the original number! Example: Is 1603 divisible by seven? Well, 3(1)+0(3)+6(2)+1(6)=21 is divisible by 7, so 1603 is.

Test #2. Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7. Example: 1603 -> 160-2(3)=154 -> 15-2(4)=7, so 1603 is divisible by 7.

*Cited : Su, Francis E., et al. “Divisibility by Seven.” Math Fun Facts. <http://www.math.hmc.edu/funfacts>.*