What are the divisors of 5991?

1, 3, 1997, 5991

There is a total of 4 positive divisors.
The sum of these divisors is 7992.
The arithmetic mean is 1998.

4 odd divisors

1, 3, 1997, 5991

How to compute the divisors of 5991?

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 5991 by each of the numbers from 1 to 5991 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)

5991 / 1 = 5991 (the remainder is 0, so 1 is a divisor of 5991)
5991 / 2 = 2995.5 (the remainder is 1, so 2 is not a divisor of 5991)
5991 / 3 = 1997 (the remainder is 0, so 3 is a divisor of 5991)
...
5991 / 5990 = 1.0001669449082 (the remainder is 1, so 5990 is not a divisor of 5991)
5991 / 5991 = 1 (the remainder is 0, so 5991 is a divisor of 5991)

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 5991 (i.e. 77.401550372069). 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 $\frac{N}{d} = D$ )

5991 / 1 = 5991 (the remainder is 0, so 1 and 5991 are divisors of 5991)
5991 / 2 = 2995.5 (the remainder is 1, so 2 is not a divisor of 5991)
5991 / 3 = 1997 (the remainder is 0, so 3 and 1997 are divisors of 5991)
...
5991 / 76 = 78.828947368421 (the remainder is 63, so 76 is not a divisor of 5991)
5991 / 77 = 77.805194805195 (the remainder is 62, so 77 is not a divisor of 5991)