Rules for Finding Divisibility

The ability to know and use the rules of divisibility is critical to being able to find and use shortcuts in mathematics. The writer considers the memorization of these rules to be critically important

For a number to be divisible by

2,

it must be an even number. That is to say, the number in the ones place is 2, 4, 6, 8, or 0.

3,

the sum of the number's digits must be divisible by 3.

4,

the last two digits of the number must be divisible by 4.

5,

the number must end in 0 or 5.

6,

it must be divisible by both 2 and 3. That is to say the number must be even and the sum of its digits is a sum that is divisible by 3.

7,

if when you drop the ones' digit and subtract 2 times the ones digit from the remaining number and the result is divisible by 7, then the original number can also be divided by 7.

8,

the number formed by the last three digits of the number can be divided by 8.

9,

the sum of the digits must be divisible by 9.

10,

the number must end in 0.

11,

you must add the alternate digits, beginning with the first digit. Next you must add the alternate digits beginning with the second. Subtract the smaller sum from the larger. If the difference is divisible by 11, then the original is also divisible by 11.

12,

the number must be divisible by both 3 and 4.

2,	it must be an even number. That is to say, the number in the ones place is 2, 4, 6, 8, or 0.
3,	the sum of the number's digits must be divisible by 3.
4,	the last two digits of the number must be divisible by 4.
5,	the number must end in 0 or 5.
6,	it must be divisible by both 2 and 3. That is to say the number must be even and the sum of its digits is a sum that is divisible by 3.
7,	if when you drop the ones' digit and subtract 2 times the ones digit from the remaining number and the result is divisible by 7, then the original number can also be divided by 7.
8,	the number formed by the last three digits of the number can be divided by 8.
9,	the sum of the digits must be divisible by 9.
10,	the number must end in 0.
11,	you must add the alternate digits, beginning with the first digit. Next you must add the alternate digits beginning with the second. Subtract the smaller sum from the larger. If the difference is divisible by 11, then the original is also divisible by 11.
12,	the number must be divisible by both 3 and 4.