How to use the divisor calculator
- Enter one positive whole number without digit-grouping commas, decimals, or exponent notation.
- Choose Calculate or press Enter. The calculator tests factor pairs only through the square root and then sorts the full list.
- Read the divisor list, number of divisors, and exact sum. Copy result exports all three values as plain text.
- Edit the number to invalidate the old list immediately, or use Clear beside the input to remove the whole calculation.
How the divisor list is found
A positive integer d is a divisor of n when n mod d = 0. If d divides n, then n ÷ d is its paired divisor.
Only candidates d with d² ≤ n need testing. Each successful pair contributes two divisors, except when d² = n; that square-root divisor is added once.
The count τ(n) is the length of the completed list and the divisor sum σ(n) adds every positive divisor. Both values are computed from the displayed exact list.
Examples
Divisors of 36
The list is 1, 2, 3, 4, 6, 9, 12, 18, 36. It contains 9 values and their sum is 91.
A prime number
For 17 the only positive divisors are 1 and 17, so the count is 2 and the sum is 18.
The number 1
One has the single positive divisor 1. Its divisor count and divisor sum are both 1.
Limits and error help
- The accepted range is 1 through 1,000,000,000,000 inclusive.
- Zero and negative integers are outside this page because the set of their integer divisors needs a different convention and is not finite for zero.
- At the upper bound, testing at most one million candidates keeps the browser task finite.
- The page lists positive divisors only; it does not duplicate them as negative divisors.
- No prime-factor tree, primality report, unbounded search, or bulk range mode is included.
- The divisor values, count, and sum are exact and are not rounded.
Frequently asked questions
Are 1 and the number always divisors?
Yes for every positive integer. They form a pair, except for n = 1 where they are the same divisor and appear once.
Why do perfect squares have an odd divisor count?
All factor pairs contain two different values except the square-root pair, whose two values are equal and are counted once.
Does a prime have exactly two divisors?
Yes: 1 and itself. This page shows that list but leaves broader prime analysis to the separate prime-factorization tool.
Are negative divisors included?
No. The result follows the common positive-divisor convention.
Why is there a one-trillion limit?
It gives a clear responsiveness ceiling for trial division in an ordinary browser.