Divisors calculator
Positive divisors: the first 40, full count, sum and proper-divisor sum.
Fill in the fields and the result will appear here automatically.
Find positive divisors of an integer n from 1 to 1000000000000, their count, their sum and the proper-divisor sum excluding n itself. Each divisor i up to √n provides its partner n/i. For a square, the coincident square root is counted once. Totals use the entire set; the main result previews only the first 40 divisors. For n = 1 the set contains just one; one is not prime.
How it works
Formula and logic
Every i up to the square root that divides n contributes both i and n ÷ i; the pair coincides for a perfect square.
Example
360 has 24 divisors adding up to 1170.
Fields and units
- Number n — unitless
How to use
- — Enter a whole number of one or more.
- — View the first 40 divisors; the full count and sums are shown separately.
- — Check the count and sum below it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: positive factor pairs, prime numbers and why one is not prime
- Limitation
- Find positive divisors of an integer n from 1 to 1000000000000, their count, their sum and the proper-divisor sum excluding n itself. Totals use the entire set; the main result previews only the first 40 divisors.
FAQ
How is this different from prime factorisation?
Factorisation gives the prime building blocks; this gives every number that divides evenly. Building one list from the other still takes work.
Why does a perfect square have an odd count?
Its square root pairs with itself, so one divisor has no distinct partner and the total comes out odd.
What makes a number perfect?
Its proper divisors add up to the number itself. Six is the smallest: one plus two plus three.
Why are numbers capped at a trillion?
For n ≤ 10¹², trial division up to √n needs at most a million checks. This is the page’s workload limit; actual time depends on the device. Larger integers also have divisors, but this tool does not accept them.