Divisors Calculator

Written byOleh Soloninupdated 5 October 2026

Number

Result

Divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Divisor pairs
1 × 360, 2 × 180, 3 × 120, 4 × 90, 5 × 72, 6 × 60, 8 × 45, 9 × 40, 10 × 36, 12 × 30, 15 × 24, 18 × 20
How many24
Sum of divisors1,170
Sum of proper divisors810
Type of numberabundant

Search to the square root, not to the number

The complete list of divisors, how many there are, their sum, and whether the number is perfect, abundant or deficient.

Divisors always come in pairs: if 6 divides 360 then so does 60. So there is no need to test every number up to the target — reaching the square root is enough, recording each partner as you go.

The sum of the divisors gives the classical classification. When the proper divisors add up to the number itself it is perfect, and only a few dozen of those are known. More makes it abundant, less makes it deficient.

How to use

Enter the number whose divisors you want.
Read the full list, the divisor pairs and how the number classifies.
Read the divisor pairs and the classification drawn from the sum of the proper divisors.

Divisors come in pairs

360 has twenty-four divisors, and they fall into twelve pairs: 1 × 360, 2 × 180, 3 × 120 and so on up to 18 × 20. That pairing is why a search only needs to run as far as the square root — the rest come free by division.

The sum of the proper divisors decides the classification. For 360 it is 810, more than the number itself, which makes it abundant. Perfect numbers, where the sum equals the number, are rare: 6, 28, 496.

Worked out with this calculator.
Number	Divisors	Sum of proper divisors	Class
6	4	6	perfect
28	6	28	perfect
97	2	1	deficient, prime
360	24	810	abundant

What this calculator shows

Every divisor in ascending order, including one and the number itself
How many there are and what they sum to
The proper-divisor sum and the classification that follows from it

What to keep in mind

Only positive divisors are listed; negative ones, technically divisors too, are omitted.
The upper bound is a hundred million so the search stays instant.

FAQs

Can I count divisors without listing them?

Factorise into primes and multiply the exponents each increased by one. For 360 = 2³ × 3² × 5 that is 4 × 3 × 2 = 24.

What makes a number perfect?

Its proper divisors add up to the number itself. Six is 1 + 2 + 3 and twenty-eight is 1 + 2 + 4 + 7 + 14. Only 52 are known — one for each known Mersenne prime, the latest found in October 2024 — and every one of them is even. For 360 the sum is 810, so 360 is abundant instead.

How many divisors does a prime have?

Exactly two: one and itself. That is the definition. One has a single divisor, which is why it counts as neither prime nor composite.

How do divisors differ from prime factors?

Prime factors are the building blocks — 360 has three distinct ones. Divisors are every number that divides it evenly, composites included, and there are twenty-four.

How many divisors does 360 have?

Twenty-four. The factorisation 2³ · 3² · 5 gives it away: add one to each exponent and multiply, 4 × 3 × 2 = 24.

Worked example

The number 360

Input: 360

Output: 24 divisors, summing to 1,170

Note: Twenty-four divisors is a lot for so small a number. That is what makes a 360° circle so easy to split — by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more.

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Result

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