Check if a number is divisible by 2–12 and any custom divisor. See divisibility rules, digit sums, prime factorization, all divisors, visual grid, and a range checker with color-coded results.
The **Divisibility Calculator** checks whether a number is divisible by 2 through 12 and by any custom divisor you enter. For each test it shows the remainder, the matching divisibility rule, and a visual pass/fail indicator, so you can see both the result and the reason behind it.
It also gives you the number's factor structure in one place: digit sum, alternating digit sum for the 11 test, prime factorization, total divisor count, and the full divisor list. That makes it useful for fraction simplification, factor hunting, and quick number-pattern checks where a plain yes/no answer is not enough.
The range grid extends the same idea across a span of numbers, which is helpful when you want to spot multiples or compare a divisor against a sequence instead of a single value. That broader view makes the page useful for both quick checks and pattern-finding exercises where repeated divisibility matters.
This calculator is useful when you want the reason behind a divisibility result, not just the yes or no. It combines the standard classroom rules with custom testing, prime factorization, and a divisor list, so it works well for homework checks, fraction simplification, and factor analysis. The range view also helps you move from one-off testing to seeing how multiples repeat across a sequence.
A number n is divisible by d if n mod d = 0. Digit-sum rule: n is divisible by 3 or 9 when the sum of its digits is divisible by 3 or 9. Alternating-sum rule: n is divisible by 11 when the alternating digit sum is divisible by 11.
Result: 360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 12.
360 has a digit sum of 9, ends in 0, and is built from 2^3 × 3^2 × 5. Those factors explain why it passes most of the standard divisibility tests.
This calculator examines an integer from several angles at once. It tests divisibility by every standard divisor from 2 through 12, reports the remainder for each one, and shows the rule that applies to that divisor. Instead of forcing you to remember whether 11 uses an alternating digit sum or whether 8 depends on the last three digits, the table keeps the rule next to the actual result.
That makes the tool useful both for learning and for verification. If a student thinks 360 should be divisible by 9, the calculator does not just confirm it. It also shows the digit sum and the remainder, so the reason is visible. If the number fails a test, the remainder immediately shows how close it was to the next multiple.
Beyond the standard checks, the calculator also handles a custom divisor and summarizes the overall factor structure of the number. The prime factorization output shows how the number is built multiplicatively, while the full divisor list and divisor count make it easier to identify common factors for fraction reduction, least common multiple work, and pattern analysis.
The range divisibility grid adds a different kind of insight. After you choose a divisor and a start and end value, the calculator highlights which numbers in that range divide evenly. This is useful for spotting multiples, checking sequences, or building intuition about how often a divisor appears across consecutive integers. Together, the rules table, factor outputs, and range grid make the tool more informative than a single divisibility checkbox.
By 2: last digit is even. By 3: digit sum divisible by 3. By 5: ends in 0 or 5. By 9: digit sum divisible by 9. By 10: ends in 0.
Double the last digit, subtract from the remaining number. If the result is divisible by 7, so is the original. For 371: 37 − 2 = 35, which is divisible by 7.
They let you test factors quickly without a full division, which is useful when simplifying fractions, checking multiples, and solving number theory problems. That speed matters when you are screening several candidate divisors or checking work by hand.
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 123 has digit sum 6, which is divisible by 3, so 123 is divisible by 3.
Divisibility rules let you test factors without performing a full division. This is especially helpful when simplifying fractions or factoring large numbers by hand.
A number is divisible by 11 if the alternating digit sum (adding and subtracting digits alternately from the right) is divisible by 11. For 1,001: 1 − 0 + 0 − 1 = 0, so it is divisible by 11.