What are the divisors of 5857?

1, 5857

There is a total of 2 positive divisors.
The sum of these divisors is 5858.
The arithmetic mean is 2929.

2 odd divisors

1, 5857

How to compute the divisors of 5857?

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 5857 by each of the numbers from 1 to 5857 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)

5857 / 1 = 5857 (the remainder is 0, so 1 is a divisor of 5857)
5857 / 2 = 2928.5 (the remainder is 1, so 2 is not a divisor of 5857)
5857 / 3 = 1952.3333333333 (the remainder is 1, so 3 is not a divisor of 5857)
...
5857 / 5856 = 1.0001707650273 (the remainder is 1, so 5856 is not a divisor of 5857)
5857 / 5857 = 1 (the remainder is 0, so 5857 is a divisor of 5857)

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 5857 (i.e. 76.53103945459). 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 $\frac{N}{d} = D$ )

5857 / 1 = 5857 (the remainder is 0, so 1 and 5857 are divisors of 5857)
5857 / 2 = 2928.5 (the remainder is 1, so 2 is not a divisor of 5857)
5857 / 3 = 1952.3333333333 (the remainder is 1, so 3 is not a divisor of 5857)
...
5857 / 75 = 78.093333333333 (the remainder is 7, so 75 is not a divisor of 5857)
5857 / 76 = 77.065789473684 (the remainder is 5, so 76 is not a divisor of 5857)