Divisors Calculator

Number

Result

Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
How many24
Sum of divisors1,170
Sum of proper divisors810
Type of numberизбыточное

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.

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 sum to itself. The first are 6 (1 + 2 + 3) and 28 (1 + 2 + 4 + 7 + 14). Only 51 are known, and every one of them is even.

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.

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 precisely why 360 was chosen for degrees in a circle — it splits neatly by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more.

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Divisors Calculator

Result

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