Divisibility Test Calculator
Enter any whole number and instantly see which divisors from 2 to 11 it is divisible by, plus the classic shortcut rule that explains each result — useful for homework, mental-math practice, and quick number-theory checks.
360 is divisible by: 2, 3, 4, 5, 6, 8, 9, 10
How does this calculator work?
A number is divisible by d if N mod d = 0. Quick rules: even last digit for 2; digit sum for 3 and 9; last two digits for 4; last digit 0 or 5 for 5; last three digits for 8; alternating digit sum for 11. Enter any whole number to instantly see which of the divisors 2–11 it passes.
Formula
How this is calculated
A number N is divisible by d if dividing N by d leaves a remainder of zero (N mod d = 0). Each divisor from 2 to 11 has a shortcut rule that avoids full long division by inspecting digits directly.
The key rules: **2** — last digit even; **3** — digit sum divisible by 3; **4** — last two digits divisible by 4; **5** — last digit 0 or 5; **6** — divisible by both 2 and 3; **8** — last three digits divisible by 8; **9** — digit sum divisible by 9; **10** — last digit 0; **11** — alternating sum of digits (+ then − from left) divisible by 11. Divisor 7 has no elegant single-digit trick, so the calculator shows the direct modular remainder.
For negative numbers, divisibility is defined by the absolute value: a remainder of zero is what matters regardless of sign. Decimals and fractions are not valid inputs — divisibility is a concept for integers only.
Frequently asked questions
Every power of 10 is congruent to 1 modulo 9 (and modulo 3), because 10 = 9 + 1. So each digit d_i contributes d_i × 10^i ≡ d_i × 1 = d_i (mod 9). The number and its digit sum therefore have the same remainder when divided by 9 — or by 3.
There is no single elegant digit-shortcut as clean as the rules for 2, 3 or 5. One method is to double the last digit and subtract from the remaining number, repeating until small — but for most practical purposes, direct division (or checking the remainder) is the simplest approach, which is what this calculator does.
This calculator covers 2–11. For larger divisors, combine smaller rules: divisible by 12 ⟺ by 3 and 4; by 15 ⟺ by 3 and 5; by 25 ⟺ last two digits divisible by 25. For primes beyond 11, direct modular arithmetic is usually the most practical approach.
Also known as
TG we-Calculate Editorial Team. (2026). Divisibility Test Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/divisibility-test-calculator
TG we-Calculate Editorial Team. "Divisibility Test Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/divisibility-test-calculator.
TG we-Calculate Editorial Team, "Divisibility Test Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/divisibility-test-calculator
@misc{wecalculate_divisibility_test_calculator, title = {Divisibility Test Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/divisibility-test-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?