

Divisibility Rules and TestsRules and to determining divisibility
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 mostfrequently 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 like the TI89 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. Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz
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 divisble by using the divisibility calculator below. Just fill in the numbers and let the divisibility calculator do the rest.
Check Divisibility
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.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 3 Rule
Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 4 Rule
Rule: A number is divisible by 4 if the number's last two digits are divisible by 4.
Use the divisibility calculator below to determine if any number is divisible by four. Type in any number that you want,
and the calculator will use the rule for divisibility by 4 to explain the result.
Ever wonder why these rules work. The test for 4 makes sense if you just break down the numbers. Think about what this rule says: "All that matters is whether or not the last two digits are divisible by 4." Let's look at why this rule is true.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 5 Rule
(another well known rule) Rule: A number is divisible by 5 if the its last digit is a 0 or 5.
Use the divisibility calculator below to determine if any number is divisible by five. Type in any number that you want,
and the calculator will use the rule for divisibility by 5 to explain the result.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 6 Rule
Since 6 is a multiple of 2 and 3, the rules for divisibility by 6 are a combination of the rule for 2 and the rule for 3. In other words, a number passes this divisibility test only if it passes the test for 2 and test for 3.
Use the divisibility calculator below to determine if any number is divisible by six. Type in any number that you want,
and the calculator will use the rule for divisibility by 6 to explain the result.
Rule A number is divisible by 6 if it is even and if the sum of its digits is divisible by 3.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 8 Rule
Rule A number passes the test for 8 if the last three digits form a number is divisible 8.
Use the divisibility calculator below to determine if any number is divisible by eight. Type in any number that you want,
and the calculator will use the rule for divisibility by 8 to explain the result.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 9 Rule
Rule A number is divisible by 9 if the sum of the digits are evenly divisible 9.
Use the divisibility calculator below to determine if any number is divisible by nine. Type in any number that you want,
and the calculator will explain whether or not it's divisible by nine based on this rule.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 10 Rule
Rule A number passes the test for 10 if its final digit is 0..
Use the divisibility calculator below to determine if any number is divisible by ten. Type in any number that you want,
and the calculator will use the rule for divisibility by 10 to explain the result.
Rules: divisible by 2  by 3  by 4  by 5 by 6  by 8  by 9  by 10  by 11  Divisibility calculator  Divisibility Calculator  Custom Divisibility Quiz Divisibility by 11 Rule
Rule A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.(This abstract and confusing sounding rule is much clearer with a few examples)
Use the divisibility calculator below to determine if any number is divisible by eleven. Type in any number that you want,
and the calculator will explain whether or not it's divisible by 11 based on this rule.
Well, at the top of this page, I told you that some rules are not actually painful at all. Some of the rules for divisibility on this page actually work better than the best graphing calculators that you can buy! 