What are the divisors of 5998?

1, 2, 2999, 5998

There is a total of 4 positive divisors.
The sum of these divisors is 9000.
The arithmetic mean is 2250.

2 even divisors

2, 5998

2 odd divisors

1, 2999

How to compute the divisors of 5998?

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 5998 by each of the numbers from 1 to 5998 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)

5998 / 1 = 5998 (the remainder is 0, so 1 is a divisor of 5998)
5998 / 2 = 2999 (the remainder is 0, so 2 is a divisor of 5998)
5998 / 3 = 1999.3333333333 (the remainder is 1, so 3 is not a divisor of 5998)
...
5998 / 5997 = 1.0001667500417 (the remainder is 1, so 5997 is not a divisor of 5998)
5998 / 5998 = 1 (the remainder is 0, so 5998 is a divisor of 5998)

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 5998 (i.e. 77.446755903653). 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 $\frac{N}{d} = D$ )

5998 / 1 = 5998 (the remainder is 0, so 1 and 5998 are divisors of 5998)
5998 / 2 = 2999 (the remainder is 0, so 2 and 2999 are divisors of 5998)
5998 / 3 = 1999.3333333333 (the remainder is 1, so 3 is not a divisor of 5998)
...
5998 / 76 = 78.921052631579 (the remainder is 70, so 76 is not a divisor of 5998)
5998 / 77 = 77.896103896104 (the remainder is 69, so 77 is not a divisor of 5998)