HesapHanem

List Divisors Calculator

Enter a whole number to see a full list of all its divisors.

How it is calculated

The tool tests every integer i from 1 up to ⌊√n⌋. Whenever n mod i = 0, both i and its partner n / i are divisors, and the partner is skipped if it equals i so that a square root is not listed twice. The list is then sorted from smallest to largest and shown as comma-separated numbers, followed by the count of divisors. Both 1 and n itself are included. The input must be a whole number from 1 to 1 000 000; zero, negatives, decimals and larger values return no result. Only positive divisors are listed; for negative divisors, just negate each one.

Worked example

List the divisors of 36. Step 1: √36 = 6, so test i = 1 to 6. Step 2: i = 1 gives 1 and 36; i = 2 gives 2 and 18; i = 3 gives 3 and 12; i = 4 gives 4 and 9; i = 5 fails; i = 6 gives 6 once, since 36 / 6 is also 6. Step 3: sort them. The tool prints 1, 2, 3, 4, 6, 9, 12, 18, 36, a count of 9.

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Common mistakes

  • Leaving out 1 or the number itself. Both are divisors, so a prime such as 97 has exactly two: 1 and 97.
  • Confusing divisors with prime factors. The prime factors of 36 are only 2 and 3, while it has nine divisors.
  • Confusing divisors with multiples. Divisors are never larger than n; multiples never smaller.
  • Expecting an even count for every number. Perfect squares such as 36 have an odd count, because the square root pairs with itself.
  • Entering a number above 1 000 000 or a decimal and expecting a list.

About this calculator

A divisor (or factor) of a whole number n is any integer that divides n with no remainder; every number's complete divisor list can be found efficiently by checking candidates only up to its square root, since divisors pair up (if d divides n, so does n divided by d), which is the standard algorithm used instead of brute-force checking every integer up to n.

Listing divisors is fundamental to number theory and shows up throughout math education and computer science — it is the basis for finding the greatest common divisor and least common multiple, identifying prime numbers (which have exactly two divisors, 1 and themselves), classifying perfect, abundant, or deficient numbers, and simplifying fractions.

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