What are the divisors of 5996?

1, 2, 4, 1499, 2998, 5996

There is a total of 6 positive divisors.
The sum of these divisors is 10500.
The arithmetic mean is 1750.

4 even divisors

2, 4, 2998, 5996

2 odd divisors

1, 1499

How to compute the divisors of 5996?

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 5996 by each of the numbers from 1 to 5996 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)

5996 / 1 = 5996 (the remainder is 0, so 1 is a divisor of 5996)
5996 / 2 = 2998 (the remainder is 0, so 2 is a divisor of 5996)
5996 / 3 = 1998.6666666667 (the remainder is 2, so 3 is not a divisor of 5996)
...
5996 / 5995 = 1.0001668056714 (the remainder is 1, so 5995 is not a divisor of 5996)
5996 / 5996 = 1 (the remainder is 0, so 5996 is a divisor of 5996)

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 5996 (i.e. 77.433842730424). 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 $\frac{N}{d} = D$ )

5996 / 1 = 5996 (the remainder is 0, so 1 and 5996 are divisors of 5996)
5996 / 2 = 2998 (the remainder is 0, so 2 and 2998 are divisors of 5996)
5996 / 3 = 1998.6666666667 (the remainder is 2, so 3 is not a divisor of 5996)
...
5996 / 76 = 78.894736842105 (the remainder is 68, so 76 is not a divisor of 5996)
5996 / 77 = 77.87012987013 (the remainder is 67, so 77 is not a divisor of 5996)