You can find a pattern that can tell whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11.

Divisibility by 10

The multiples are 10, 20, 30, 40, 50, 60, ... . Each of these numbers has 0 in the ones place.

All such numbers are divisible by 10. If a number has 0 in the ones place then it is divisible by 10.

Divisibility by 5

The multiples are 5, 10, 15, 20, 25, 30, 35, ... . All these numbers have either 0 or 5 in their ones place. These numbers are divisible by 5.

A number which has either 0 or 5 in its ones place is divisible by 5, other numbers leave a remainder.

Divisibility by 2

Some multiples of 2 are 10, 12, 14, 16 ... and also numbers like 2410, 4356, 1358, 2972, 5974. These numbers have only the digits 0, 2, 4, 6, 8 in the ones place.

A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.

Divisibility by 3

The numbers 21, 27, 36, 54, 219 are divisible by 3.

If the sum of the digits is a multiple of 3, then the number is divisible by 3.

Divisibility by 6

If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Divisibility by 4

A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4. Divisibility for 1 or 2 digit numbers by 4 has to be checked by actual division.

Divisibility by 8

A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8. The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division.

Divisibility by 9

The multiples of 9 are 9, 18, 27, 36, 45, 54, ... There are other numbers like 4608, 5283 that are also divisible by 9. If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.

Divisibility by 11

The numbers 308, 1331 and 61809 are all divisible by 11. To check the divisibility of a number by 11, the rule is, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.