What are the divisors of 5982?

1, 2, 3, 6, 997, 1994, 2991, 5982

There is a total of 8 positive divisors.
The sum of these divisors is 11976.
The arithmetic mean is 1497.

4 even divisors

2, 6, 1994, 5982

4 odd divisors

1, 3, 997, 2991

How to compute the divisors of 5982?

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 5982 by each of the numbers from 1 to 5982 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)

5982 / 1 = 5982 (the remainder is 0, so 1 is a divisor of 5982)
5982 / 2 = 2991 (the remainder is 0, so 2 is a divisor of 5982)
5982 / 3 = 1994 (the remainder is 0, so 3 is a divisor of 5982)
...
5982 / 5981 = 1.0001671961211 (the remainder is 1, so 5981 is not a divisor of 5982)
5982 / 5982 = 1 (the remainder is 0, so 5982 is a divisor of 5982)

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 5982 (i.e. 77.343390150678). 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 $\frac{N}{d} = D$ )

5982 / 1 = 5982 (the remainder is 0, so 1 and 5982 are divisors of 5982)
5982 / 2 = 2991 (the remainder is 0, so 2 and 2991 are divisors of 5982)
5982 / 3 = 1994 (the remainder is 0, so 3 and 1994 are divisors of 5982)
...
5982 / 76 = 78.710526315789 (the remainder is 54, so 76 is not a divisor of 5982)
5982 / 77 = 77.688311688312 (the remainder is 53, so 77 is not a divisor of 5982)