What are the divisors of 5999?

1, 7, 857, 5999

There is a total of 4 positive divisors.
The sum of these divisors is 6864.
The arithmetic mean is 1716.

4 odd divisors

1, 7, 857, 5999

How to compute the divisors of 5999?

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 5999 by each of the numbers from 1 to 5999 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)

5999 / 1 = 5999 (the remainder is 0, so 1 is a divisor of 5999)
5999 / 2 = 2999.5 (the remainder is 1, so 2 is not a divisor of 5999)
5999 / 3 = 1999.6666666667 (the remainder is 2, so 3 is not a divisor of 5999)
...
5999 / 5998 = 1.0001667222407 (the remainder is 1, so 5998 is not a divisor of 5999)
5999 / 5999 = 1 (the remainder is 0, so 5999 is a divisor of 5999)

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 5999 (i.e. 77.453211682925). 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 $\frac{N}{d} = D$ )

5999 / 1 = 5999 (the remainder is 0, so 1 and 5999 are divisors of 5999)
5999 / 2 = 2999.5 (the remainder is 1, so 2 is not a divisor of 5999)
5999 / 3 = 1999.6666666667 (the remainder is 2, so 3 is not a divisor of 5999)
...
5999 / 76 = 78.934210526316 (the remainder is 71, so 76 is not a divisor of 5999)
5999 / 77 = 77.909090909091 (the remainder is 70, so 77 is not a divisor of 5999)