HesapHanem

Divisor Count Calculator

Find all divisors of a number along with their count and total sum.

How it is calculated

A divisor of n is a whole number that divides it with no remainder. The tool tests every i from 1 while i × i ≤ n; each i that divides n gives two divisors, i and n ÷ i (counted once if they are equal, as for perfect squares). It then sorts them and reports the count, the sum of all divisors (including 1 and n itself) and the list. Only whole numbers of 1 or more are accepted. If there are more than 40 divisors, the list shows the first 40 followed by an ellipsis, though the count and sum still cover all of them.

Worked example

Take n = 60. Testing i = 1 to 7 (since 8 × 8 is above 60), the divisors that work are 1, 2, 3, 4, 5, 6, each paired with 60, 30, 20, 15, 12, 10. Sorted, the list is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60: 12 divisors. Their sum is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60 = 168.

Try this example →

Common mistakes

  • Forgetting that 1 and the number itself are divisors. The count for 60 is 12, not 10.
  • Confusing divisors with prime factors. 60 has only the prime factors 2, 3 and 5, but twelve divisors in total.
  • Entering 0, a negative number or a decimal. Only whole numbers from 1 are valid, so there is no result.
  • Reading the sum as the sum of proper divisors. The sum here includes the number itself; subtract n for the proper-divisor sum.
  • Assuming a long list is complete. Beyond 40 divisors only the first 40 are displayed, though the count is exact.

About this calculator

This calculator lists every divisor of a whole number, along with how many divisors it has and what they add up to — found by testing which numbers divide evenly into it, a direct application of the same factoring concepts used to compute a number's prime factorization.

Students use it to check math homework on factors and divisibility, and it comes up in number theory topics like identifying perfect numbers (where the divisors excluding the number itself sum to the number) or finding common factors between two numbers.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Only whole numbers from 1 upward are accepted, and the list shown stops after the first 40 divisors with an ellipsis, though the count and sum still cover all of them. A handy use is spotting prime numbers: a prime has exactly 2 divisors. If the divisor sum equals twice the number, you have found a perfect number such as 6 or 28. Have you found a number with a surprising divisor count? Share it with us.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators