What are the divisors of 5804?

1, 2, 4, 1451, 2902, 5804

There is a total of 6 positive divisors.
The sum of these divisors is 10164.
The arithmetic mean is 1694.

4 even divisors

2, 4, 2902, 5804

2 odd divisors

1, 1451

How to compute the divisors of 5804?

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 5804 by each of the numbers from 1 to 5804 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)

5804 / 1 = 5804 (the remainder is 0, so 1 is a divisor of 5804)
5804 / 2 = 2902 (the remainder is 0, so 2 is a divisor of 5804)
5804 / 3 = 1934.6666666667 (the remainder is 2, so 3 is not a divisor of 5804)
...
5804 / 5803 = 1.0001723246597 (the remainder is 1, so 5803 is not a divisor of 5804)
5804 / 5804 = 1 (the remainder is 0, so 5804 is a divisor of 5804)

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 5804 (i.e. 76.183987818964). 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 $\frac{N}{d} = D$ )

5804 / 1 = 5804 (the remainder is 0, so 1 and 5804 are divisors of 5804)
5804 / 2 = 2902 (the remainder is 0, so 2 and 2902 are divisors of 5804)
5804 / 3 = 1934.6666666667 (the remainder is 2, so 3 is not a divisor of 5804)
...
5804 / 75 = 77.386666666667 (the remainder is 29, so 75 is not a divisor of 5804)
5804 / 76 = 76.368421052632 (the remainder is 28, so 76 is not a divisor of 5804)