Workings

Divisibility Checker (Rules for 2 to 12)

Enter a number — even a very long one — to see which of 2 to 12 divide it, and why.

Divisibility Checker

All fields are required unless marked “optional”.

Digits only, up to 500 digits. Commas and spaces are ignored.

Your result will appear hereFill in the fields and press “Check”.

Formula

  • by 3 or 9: the digit sum is divisible by 3 or 9
  • by 4 or 8: the last 2 or 3 digits are divisible by 4 or 8
  • by 11: the alternating digit sum is divisible by 11
  • by 2, 5, 10: the last digit is even, 0 or 5, or 0
  • by 6: divisible by both 2 and 3; by 12: divisible by both 3 and 4

Each rule checks a small part of the number instead of dividing the whole thing.

Worked examples

123456

Number
123456

Divisible by

2, 3, 4, 6, 8, 12

Number tested: 123456

Digit sum: 21

Number of digits: 6

A number with a custom divisor

Number
1001
Your own divisor
13

Divisible by

11, 13

Number tested: 1001

Digit sum: 2

Number of digits: 4

How it works

Divisibility rules let you test a number without long division. For 3 and 9, add the digits: a number is divisible by 3 (or 9) exactly when its digit sum is. For 4 and 8, only the last two (or three) digits matter, because 100 is divisible by 4 and 1,000 by 8. For 11, subtract and add the digits alternately from the right.

This checker applies every rule from 2 to 12, shows the intermediate figure it used for each, and confirms the answer by an exact remainder calculation. It handles numbers of up to 500 digits using exact big-integer arithmetic, far beyond what a normal calculator can hold, and ignores commas, spaces and a leading minus sign.

For the full list of factors use the Prime Factorization Calculator. The Remainder Calculator gives the actual remainder for any divisor, and the HCF and LCM Calculator finds the greatest common divisor of two numbers.

Assumptions and limits

  • Whole numbers only, up to 500 digits. The sign is ignored.
  • The rules for 7 and 13 are not offered; use the custom divisor box, which divides exactly.
Prime Factorization CalculatorBreak a number into prime factors, with exponent form, divisor count and sum of divisors.Prime Number CheckerCheck whether a number is prime, with its smallest factor and the previous and next primes.Remainder CalculatorDivide whole numbers to get the quotient and remainder, including how negatives behave.HCF and LCM CalculatorHighest common factor (GCD) and lowest common multiple of two or more numbers, with prime factors.Fraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers, simplified automatically.

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