What are the divisors of 5981?

1, 5981

There is a total of 2 positive divisors.
The sum of these divisors is 5982.
The arithmetic mean is 2991.

2 odd divisors

1, 5981

How to compute the divisors of 5981?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5981 by each of the numbers from 1 to 5981 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5981 / 1 = 5981 (the remainder is 0, so 1 is a divisor of 5981)
5981 / 2 = 2990.5 (the remainder is 1, so 2 is not a divisor of 5981)
5981 / 3 = 1993.6666666667 (the remainder is 2, so 3 is not a divisor of 5981)
...
5981 / 5980 = 1.0001672240803 (the remainder is 1, so 5980 is not a divisor of 5981)
5981 / 5981 = 1 (the remainder is 0, so 5981 is a divisor of 5981)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5981 (i.e. 77.336925203941). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5981 / 1 = 5981 (the remainder is 0, so 1 and 5981 are divisors of 5981)
5981 / 2 = 2990.5 (the remainder is 1, so 2 is not a divisor of 5981)
5981 / 3 = 1993.6666666667 (the remainder is 2, so 3 is not a divisor of 5981)
...
5981 / 76 = 78.697368421053 (the remainder is 53, so 76 is not a divisor of 5981)
5981 / 77 = 77.675324675325 (the remainder is 52, so 77 is not a divisor of 5981)