Calculators
Divisor Calculator
Find every divisor of a whole number with divisor count, sum of divisors, aliquot classification, and Euler’s totient locally in your browser.
Enter a whole number from 1 to 1 trillion to list its divisors and see its divisor count, sum of divisors, aliquot classification, and Euler's totient. The calculation runs locally in your browser; your value is not uploaded or stored.
See the complete divisor picture of any whole number.
A divisor of n is a whole number that divides it with no remainder. Enter a number from 1 to 1 trillion. The calculator reports the divisor count tau(n), the full divisor list when there are 200 or fewer divisors, the sum of divisors sigma(n), the sum of proper divisors (all divisors except n itself), whether the number is deficient, perfect, or abundant, and Euler’s totient phi(n), the count of integers from 1 to n that share no common factor with n. Everything comes from the prime factorization: tau is the product of (exponent + 1), sigma is the product of (p^(exponent + 1) − 1) / (p − 1), and phi is n multiplied by (1 − 1/p) for each distinct prime. For example, 12 = 2² × 3 has divisors 1, 2, 3, 4, 6, 12, tau(12) = 6, sigma(12) = 28, a proper-divisor sum of 16 that makes 12 abundant, and phi(12) = 4 (the integers 1, 5, 7, and 11). All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is a divisor?
A divisor of a whole number n is a whole number that divides it evenly, leaving no remainder. The divisors of 12 are 1, 2, 3, 4, 6, and 12. Every whole number from 1 upward has at least two divisors: 1 and itself.
How does the divisor calculator work?
It prime-factorizes the number by trial division, then derives everything from the factorization. The divisor count is the product of (exponent + 1). The sum of divisors is the product of (p^(exponent + 1) − 1) / (p − 1) over the prime factors. The divisor list is generated from all combinations of the prime powers and is shown when it has 200 or fewer entries. Euler’s totient is n multiplied by (1 − 1/p) for each distinct prime p.
What are abundant, perfect, and deficient numbers?
Compare the sum of proper divisors (all divisors except the number itself) with the number. If the sum is larger, the number is abundant, like 12 whose proper divisors sum to 16. If it is equal, the number is perfect, like 6 (1 + 2 + 3 = 6) and 28 (1 + 2 + 4 + 7 + 14 = 28). If it is smaller, the number is deficient, like 10 whose proper divisors sum to 8.
What is Euler’s totient?
Euler’s totient phi(n) counts the integers from 1 to n that share no common factor with n. phi(12) = 4 because only 1, 5, 7, and 11 are coprime to 12. For a prime p, phi(p) = p − 1, and phi(1) = 1 by convention.
Which inputs are accepted?
Enter a whole number from 1 to 1,000,000,000,000 (one trillion) using digits only. Decimals, negative numbers, scientific notation, zero, and values above the limit show a clear error instead of a result.
Do my numbers stay private?
Yes. The divisor analysis and copy action run locally in your browser. CodeASystem does not upload or store the value you enter.