Sum of Divisors Calculator
Calculate the sum of all positive divisors, proper divisor sum, divisor count, prime factorization, and perfect/abundant/deficient classification.
Sum of all divisors and proper divisors
The English intent for sum of divisors overlaps factor calculators and the sigma function. Users need the sum of all positive divisors first, then the proper divisor sum and classification.
The sigma function adds every positive divisor of n.
- Enter a positive integer up to 10,000,000.
- Read the sum of all divisors and the proper divisor sum.
- Use the classification to identify perfect, abundant, deficient, prime, and one cases.
Classification by proper divisor sum
| Number | Sum of all divisors | Proper divisor sum | Class |
|---|---|---|---|
| 6 | 12 | 6 | perfect |
| 12 | 28 | 16 | abundant |
| 13 | 14 | 1 | prime / deficient |
| 28 | 56 | 28 | perfect |
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Find all positive factors of a number, factor pairs, prime factorization, factor count, sum of factors, proper factors, and number type.
Break an integer into prime factors, see repeated factors, canonical exponent form, trial-division steps, and the total number of positive factors.
Check whether a whole number is prime, composite, 0, or 1. Shows the smallest factor for composite numbers and links to full factorization.
Generate all prime numbers up to N with a Sieve of Eratosthenes grid, prime-count summary, and twin-prime pairs.