What are the divisors of 5805?

1, 3, 5, 9, 15, 27, 43, 45, 129, 135, 215, 387, 645, 1161, 1935, 5805

There is a total of 16 positive divisors.
The sum of these divisors is 10560.
The arithmetic mean is 660.

16 odd divisors

1, 3, 5, 9, 15, 27, 43, 45, 129, 135, 215, 387, 645, 1161, 1935, 5805

How to compute the divisors of 5805?

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 5805 by each of the numbers from 1 to 5805 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)

5805 / 1 = 5805 (the remainder is 0, so 1 is a divisor of 5805)
5805 / 2 = 2902.5 (the remainder is 1, so 2 is not a divisor of 5805)
5805 / 3 = 1935 (the remainder is 0, so 3 is a divisor of 5805)
...
5805 / 5804 = 1.000172294969 (the remainder is 1, so 5804 is not a divisor of 5805)
5805 / 5805 = 1 (the remainder is 0, so 5805 is a divisor of 5805)

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 5805 (i.e. 76.190550595202). 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 $\frac{N}{d} = D$ )

5805 / 1 = 5805 (the remainder is 0, so 1 and 5805 are divisors of 5805)
5805 / 2 = 2902.5 (the remainder is 1, so 2 is not a divisor of 5805)
5805 / 3 = 1935 (the remainder is 0, so 3 and 1935 are divisors of 5805)
...
5805 / 75 = 77.4 (the remainder is 30, so 75 is not a divisor of 5805)
5805 / 76 = 76.381578947368 (the remainder is 29, so 76 is not a divisor of 5805)