Test of Divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

By 2

A number is divisible by 2, when the digit at ones place is 0, 2, 4, 6 or 8. e.g., 3582, 460, 28, 352, ...., Whereas, 2345, 4299 are not divisible by 2.

By 3

A number is divisible by 3 only, when the sum of its digits is divisible by 3. e.g., 453 = 4 + 5 + 3 = 12, 12 is divisible by 3. So, 453 is also divisible by 3. Whereas, 652 = 6 + 5 + 2 = 13, 13 is not divisible by 3. So, 652 is not divisible by 3.

By 4

A number is divisible by 4, if the number formed with its last two digits is divisible by 4. e.g., 784936 is divisible by 4, since 36 is divisible by 4. 423441 is not divisible by 4, since 41 is not divisible by 4.

By 5

A number is divisible by 5 when the digit at ones place is 0 or 5. e.g., 34970 and 25685 are both divisible by 5. Whereas, 25654, 9521, 3723 are not divisible by 5.

By 6

A number is divisible by 6, if it is divisible both by 2 and 3. 3672 is divisible by 6 as it is divisible by both 2 and 3. 4586 is not divisible by 6 as it is not divisible by 3.

By 7

A number is divisible by 7, when the difference between twice the digit at ones place and the number formed by the remaining digits is either 0 or a number divisible by 7. e.g., 658 is divisible by 7 as 65 - (2 x 8) = 65 - 16 = 49 is divisible by 7, 349 is not divisible by 7 as 34 - (2 x 9) = 34 - 18 = 16 is not divisible by 7.

By 8

A number is divisible by 8 only when the number formed by its last 3 digit is divisible by 8. e.g., 485120 is divisible by 8, since 120 is divisible by 8. 364940 is not divisible by 8, since 940 is not divisible by 8.

By 9

A number is divisible by 9, if the sum of its digits is divisible by 9. e.g., 812745 is divisible by 9, since the sum of its digits 8 + 1 + 2 + 7 + 4 + 5 = 27 is divisible by 9. 432512 is not divisible by 9, since the sum of its digits 4 + 3 + 2 + 5 + 1 + 2 = 17 is not divisible by 9.

By 10

A number is divisible by 10 when the digit at ones place is 0. e.g., 42570 is divisible by 10. Whereas 39745 is not divisible by 10.

By 11

A number is divisible by 11, if the difference of the Sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11. e.g., 30426 is divisible by 11, since (3+ 4 + 6) - (0 + 2) = 13 – 2 = 11 is divisible by 11. 345912 is not divisible by 11, since (4 + 9 + 2) - (3 + 5 + 1) = 15 - 9 = 6 is not divisible by 11.