Enter any whole number and the Divisibility Test Calculator checks whether it's divisible by 2 through 12 — all at once. Pick a specific divisor or test all of them simultaneously. You'll see a clear Yes/No result for each divisor along with the divisibility rule that explains why.
Divisors That Divide Evenly
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Divisors That Do Not Divide Evenly
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Result
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A divisibility test is a shortcut rule that lets you determine whether one number divides evenly into another — without performing full long division. For example, a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). These rules are especially helpful for mental math and simplifying fractions.
For 2: the last digit must be 0, 2, 4, 6, or 8. For 4: the last two digits must form a number divisible by 4. For 8: the last three digits must form a number divisible by 8. Each rule works because 2, 4, and 8 are powers of 2 and our number system is base-10.
A number is divisible by 3 if the sum of all its digits is divisible by 3. Similarly, a number is divisible by 9 if the digit sum is divisible by 9. For example, 18 has digit sum 1+8=9, so it's divisible by both 3 and 9. This works because 10 ≡ 1 (mod 3) and (mod 9), so only the digit sum matters.
The rule for 7 is less intuitive: double the last digit, subtract it from the rest of the number, and check if the result is divisible by 7. For example, for 161: double the last digit (1×2=2), subtract from 16 to get 14, which is divisible by 7. Repeat as needed for larger numbers.
Alternately add and subtract digits from left to right. If the result is 0 or divisible by 11, the number is divisible by 11. For example, 1111: 1−1+1−1=0, so yes. But 111: 1−1+1=1, which is not divisible by 11, so 111 is not divisible by 11.
A number is divisible by 6 if and only if it is divisible by both 2 and 3. That means it must be even (last digit is 0, 2, 4, 6, or 8) AND its digit sum must be divisible by 3. For example, 48 is even and 4+8=12 is divisible by 3, so 48 is divisible by 6.
Divisibility tests help you quickly simplify fractions, find factors, determine if a number is prime, and solve problems involving multiples — all without a calculator. They're fundamental tools in number theory, taught in school arithmetic, and used frequently in competitive mathematics.
Yes — this calculator supports whole numbers up to 999,999,999 (nearly one billion). For all inputs, it applies the standard divisibility rules and also verifies results mathematically using the remainder of division, so results are always accurate.