What are the divisors of 5855?

1, 5, 1171, 5855

There is a total of 4 positive divisors.
The sum of these divisors is 7032.
The arithmetic mean is 1758.

4 odd divisors

1, 5, 1171, 5855

How to compute the divisors of 5855?

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 5855 by each of the numbers from 1 to 5855 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)

5855 / 1 = 5855 (the remainder is 0, so 1 is a divisor of 5855)
5855 / 2 = 2927.5 (the remainder is 1, so 2 is not a divisor of 5855)
5855 / 3 = 1951.6666666667 (the remainder is 2, so 3 is not a divisor of 5855)
...
5855 / 5854 = 1.0001708233686 (the remainder is 1, so 5854 is not a divisor of 5855)
5855 / 5855 = 1 (the remainder is 0, so 5855 is a divisor of 5855)

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 5855 (i.e. 76.517971745205). 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 $\frac{N}{d} = D$ )

5855 / 1 = 5855 (the remainder is 0, so 1 and 5855 are divisors of 5855)
5855 / 2 = 2927.5 (the remainder is 1, so 2 is not a divisor of 5855)
5855 / 3 = 1951.6666666667 (the remainder is 2, so 3 is not a divisor of 5855)
...
5855 / 75 = 78.066666666667 (the remainder is 5, so 75 is not a divisor of 5855)
5855 / 76 = 77.039473684211 (the remainder is 3, so 76 is not a divisor of 5855)