Divisibility Test

0 & 1 - All numbers are divisible by 0 and 1.

2 - The number ends in 0, 2, 4, 6, or 8

3462350971235735692 <- Divisible by 2

3 - The sum of all the digits is divisible by 3.

27336 = 2 + 7 + 3 + 3 + 6 = 21/3 = 7 <- Divisible by 3

4 - The last two digits are divisible by 4.

324154123451251324536 = 36/4 = 9 <- Divisible by 4

5 - The number ends in 0 or 5.

1237456918723455 <- Divisible by 5

6 - Use the rules for 2 and 3. If it ends in 0, 2, 4, 6, or 8 and the sum of the digits is divisible by three then so is it.

542718 = 27/3 = 9, and ends in 8 <- Divisible by 6

7 - 1 * 1s digit + 3 * 10s digit + 2 * 100s digit - 1 * 1000s digit - 3 * 10000s digit - 2 * 100000s digit + 1 * 1000000s digit ... If the sum is divisible by 7 then so is the number. The pattern is multiply each digit starting at 1s by 1,3,2,1,3,2,1,3,2 in order, alternating +, -, +, ... for each group of 132.

7108402 = +(1*2)+(3*0)+(2*4)-(1*8)-(3*0)-(2*1)+(1*7) = 7 <- Divisible by 7

8 - If the hundreds digit is even, check if the last two digits are a multiple of 8.
- If the hundreds digit is odd, check if the last two digits are a multiple of 4 but not 8.

12341361345123515832 - 8 = even - 32/8 = 4 <- Divisible by 8
6234512346312 - 3 = odd - 12/4 = 3, 12/8 = 1.5 <- Divisible by 8

9 - The sum of the digits are divisible by 9

819 = 8 + 1 + 9 = 18/9 = 2 <- Divisible by 9

10 - The last digit is 0.

18947091235698762530 <- divisible by 10

11 - Formulate the digits in reverse order alternating - and + starting with -. If the sum is divisible by 11 so is the number. Also if the number is an odd numbered palindrome with a central even digit the number is divisible by 11.
913891 = 1 - 9 + 8 - 3 + 1 - 9 = -11 <- Divisible by 11
123456787654321 < Divisible by 11