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Divisibility of integers by small integers

Divisibility by 2
An integer is divisible by 2 if the integer is even.

Divisibility by 3
An integer is divisible by 3 if the sum of its digits is divisible by 3.

Proof
Problems

Divisibility by 4
An integer with at least two digits is divisible by 4 if its last two digits as a number is divisible by 4.

Proof
Problems

Divisibility by 5
An integer is divisible by 5 if if its last digit is 0 or 5.

Divisibility by 6
An integer is divisible by 6 if it is divisible by 2 and by 3.

Problems

Divisibility by 8
An integer with at least three digits is divisible by 8 if its last three digits as a number is divisible by 8.

Proof
Problems

Divisibility by 9
An integer is divisible by 9 if the sum of its digits is divisible by 9.

Proof
Problems

Divisibility by 10
An integer is divisible by 10 if its last digit is 0.

Divisibility by 11
Add all digits in the odd positions, and add all digits in the even positions. If the difference of the sums is divisible by 11 then the integer is divisible by 11.

Proof
Problems