Divisibility Checker
This tool checks whether a given number is divisible by any integer from 2 to 12. Enter your number and the checker instantly displays which divisors divide evenly into it, along with the quotient. Divisibility is a fundamental concept in number theory and mathematics education. Understanding whether numbers divide evenly is essential for simplifying fractions, finding common factors, factorising numbers, and solving problems in arithmetic and algebra. This checker also explains the mathematical rule for each divisor, showing you both the result and the reasoning behind it, making it useful for learning and verification.
Divisibility rules
| Divisor | Rule |
|---|---|
| 2 | Number is even (ends in 0, 2, 4, 6, or 8) |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Ends in 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 7 | No simple rule; requires calculation |
| 8 | Last three digits form a number divisible by 8 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Ends in 0 |
| 11 | Alternating sum of digits is divisible by 11 or equals zero |
| 12 | Divisible by both 3 and 4 |
Divisibility: frequently asked questions
What does divisibility mean?
A number is divisible by another number if it divides evenly with no remainder. For example, 15 is divisible by 3 because 15 divided by 3 equals 5 with no remainder. You can check divisibility using the modulo operation: if n % d = 0, then n is divisible by d.
What are divisibility rules?
Divisibility rules are shortcuts to determine if a number is divisible by another without actually performing the division. For example, a number is divisible by 2 if its last digit is even. A number is divisible by 3 if the sum of its digits is divisible by 3. These rules save time and are useful in mental arithmetic.
Why are divisibility rules useful?
Divisibility rules help you quickly identify factors of a number, simplify fractions, solve word problems, and perform mental calculations. They are also fundamental in number theory and understanding properties of integers.
What is the divisibility rule for 3?
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 123 has digits 1, 2, 3. Their sum is 6, which is divisible by 3, so 123 is divisible by 3. Indeed, 123 / 3 = 41.
What is the divisibility rule for 11?
A number is divisible by 11 if the alternating sum of its digits (first digit minus second plus third minus fourth, etc.) is divisible by 11 or equals zero. For example, 121 has alternating sum 1 - 2 + 1 = 0, so it is divisible by 11. Indeed, 121 / 11 = 11.
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.