We use the notation a/b to say “a divides b”. For example, 2/10 would tell us that “2 divides 10”.

Divisibility by two: If the last digit is even, the original number is divisible by 2.

Example that works 314

Example that doesn’t work 413

**Divisibility by three: ** If the sum of the digits is divisible by 3, then the original number is divisible by 3.

Example that works 315

Example that doesn’t work 314

**Divisibility by four: ** If the last two digits form a number that is divisible by 4, then the original number is divisible by 5.

Example that works 316

Example that doesn’t work 315

**Divisibility by five: ** If the last digit is either a 0 or 5, then the original number is divisible by 5.

Example that works 320

Example that doesn’t work 513

**Divisibility by six: ** If the number is divisible by 2 and 3, then it is divisible by 6.

Example that works 414

Example that doesn’t work 314

**Divisibility by seven: **Doesn’t work. Just preform the division.

**Divisibility by eight: ** if the last three digits form a number that is divisible by 8, then the original number is divisible by 9.** **

Example that works 1096

Example that doesn’t work 403316

**Divisibility by nine:** If the sum of the digits is divisible by 9, then the original number is divisible by 9.

Example that works 315

Example that doesn’t work 317

**Divisibility by ten: ** If the last digit is 0, then the original number is divisible by ten.

Example that works 520

Example that doesn’t work 523

**Divisibility by eleven: **Find the sum of the odd-numbered digits (odd sum) and the sum of the even numbered digits (even sum). Take the difference between odd sum and even sum. If this difference is divisible by 11, then the original number is divisible by 11.

**Divisibility by twelve: **If the number is divisible by 3 and 4, then it is divisible by 12.

Example that works 1308

Example that doesn’t 1433