Rules, rules, rules -- No one likes to follow rules, but sometimes there are good rules, like the ones that allow you to do less work! Well, these are exactly the kind of rules that you find on this page. There are many shortcuts or tricks that allow you to test whether a number, or dividend, is divisible by a given divisor. This page focuses on the most-frequently studied divisibility rules which involve divisibility by 2,4,5,6,8,9, 10 and 11.

### A word of caution about hand held calculators

Keep this in mind before you buy graphing calculator: Even many of the best graphing calculators or this free online graphing calculator lose their accuracy when they start dividing large numbers such as 12,347,496,132. Try to divide that large number by 11. If your calculator outputs that 12,347,496,132 is divisible by 11, your calculator IS WRONG (Look at the last example at the bottom for details). When you're dealing with exceedingly large numbers, you should rely, whenever possible, on the rules on this page rather than a scientific or a graphing calculator.

So, you may be asking yourself why is this page's calculator more accurate than that graphing calculator you bought?

- The answer is : the calculators on this page use the rules for divisibility to calculate their answers (instead of the division algorithm). Your hand held calculator uses algorithms that work for all numbers and, if you're really interested, in learning more about why computers (not just calculators) do not accurately divide huge numbers look up floating point error, sometimes called rounding error.

### Divisibility Calculator

If you do not have the time or inclination to use the rules below, you can check to see if two numbers are divisible by using the divisibility calculator below. Just fill in the numbers and let the divisibility calculator do the rest.

### Divisibility by 2 Rule

Almost everyone is familiar with this rule which states that any even number can be divided by 2. Even numbers are multiples of 2. A number is even if ends in 0,2,4,6, or 8.

Use the divisibility calculator below to determine if any number is divisible by two. Type in any number that you want, and the calculator will use the rule for divisibility by 2 to explain the result.

See what the rule for divisibility by two has to say about the following number:

**Examples** of numbers that **are even ** and therefore pass this divisibility test

- 2
- 0
- 4
- -2
- -312
- 31,102

**Examples** of numbers that are **do not pass this divisibility test** because they are not even.

- 3
- -103
- 1.50
- 221