What are the divisors of 5997?

1, 3, 1999, 5997

There is a total of 4 positive divisors.
The sum of these divisors is 8000.
The arithmetic mean is 2000.

4 odd divisors

1, 3, 1999, 5997

How to compute the divisors of 5997?

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 5997 by each of the numbers from 1 to 5997 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)

5997 / 1 = 5997 (the remainder is 0, so 1 is a divisor of 5997)
5997 / 2 = 2998.5 (the remainder is 1, so 2 is not a divisor of 5997)
5997 / 3 = 1999 (the remainder is 0, so 3 is a divisor of 5997)
...
5997 / 5996 = 1.0001667778519 (the remainder is 1, so 5996 is not a divisor of 5997)
5997 / 5997 = 1 (the remainder is 0, so 5997 is a divisor of 5997)

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 5997 (i.e. 77.440299586197). 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 $\frac{N}{d} = D$ )

5997 / 1 = 5997 (the remainder is 0, so 1 and 5997 are divisors of 5997)
5997 / 2 = 2998.5 (the remainder is 1, so 2 is not a divisor of 5997)
5997 / 3 = 1999 (the remainder is 0, so 3 and 1999 are divisors of 5997)
...
5997 / 76 = 78.907894736842 (the remainder is 69, so 76 is not a divisor of 5997)
5997 / 77 = 77.883116883117 (the remainder is 68, so 77 is not a divisor of 5997)