Divisors Calculator
All divisors of a number, their sum and factor pairs.
About this tool
Enter a whole number up to 10 trillion. The tool lists all its divisors, their count and sum, the factor pairs, the prime factorisation, the number of even and odd divisors, and whether the number is prime, perfect, abundant or deficient.
Divisors and special numbers
A divisor (or factor) of n divides it with no remainder. The divisors of 28 are 1, 2, 4, 7, 14 and 28, and they pair up to multiply to n: 1 ร 28, 2 ร 14, 4 ร 7. The number of divisors comes straight from the prime factorisation: if n = p^a ร q^b ร โฆ, it has (a + 1)(b + 1)โฆ divisors. 360 = 2ยณ ร 3ยฒ ร 5 has 4 ร 3 ร 2 = 24, which is one reason it was chosen for degrees in a circle. Adding the proper divisors (all except n itself) classifies a number. If they sum to n, it's perfect: 6, 28, 496 and 8,128 are the first four, known since Euclid. If they sum to more, it's abundant (12: 1 + 2 + 3 + 4 + 6 = 16); if less, deficient (every prime). Divisors are useful for simplifying fractions, splitting things into equal groups, working out rows and columns for layouts, and number puzzles. Honest limits: trial division is instant up to 10 trillion but isn't how very large numbers are factored. The prime number checker and the GCD and LCM calculator are related.
Frequently asked questions
How do I find all the divisors of a number?
Test every number up to its square root; each one that divides evenly gives a pair of divisors.
What is a perfect number?
A number whose proper divisors add up to itself, such as 6 (1 + 2 + 3) and 28.
How many divisors does 360 have?
24, since 360 = 2ยณ ร 3ยฒ ร 5 gives (3+1)(2+1)(1+1).
What is an abundant number?
One whose proper divisors add up to more than the number, like 12.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.