What are the divisors of 5983?

1, 31, 193, 5983

There is a total of 4 positive divisors.
The sum of these divisors is 6208.
The arithmetic mean is 1552.

4 odd divisors

1, 31, 193, 5983

How to compute the divisors of 5983?

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 5983 by each of the numbers from 1 to 5983 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)

5983 / 1 = 5983 (the remainder is 0, so 1 is a divisor of 5983)
5983 / 2 = 2991.5 (the remainder is 1, so 2 is not a divisor of 5983)
5983 / 3 = 1994.3333333333 (the remainder is 1, so 3 is not a divisor of 5983)
...
5983 / 5982 = 1.0001671681712 (the remainder is 1, so 5982 is not a divisor of 5983)
5983 / 5983 = 1 (the remainder is 0, so 5983 is a divisor of 5983)

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 5983 (i.e. 77.349854557071). 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 $\frac{N}{d} = D$ )

5983 / 1 = 5983 (the remainder is 0, so 1 and 5983 are divisors of 5983)
5983 / 2 = 2991.5 (the remainder is 1, so 2 is not a divisor of 5983)
5983 / 3 = 1994.3333333333 (the remainder is 1, so 3 is not a divisor of 5983)
...
5983 / 76 = 78.723684210526 (the remainder is 55, so 76 is not a divisor of 5983)
5983 / 77 = 77.701298701299 (the remainder is 54, so 77 is not a divisor of 5983)