What are the divisors of 5861?

1, 5861

There is a total of 2 positive divisors.
The sum of these divisors is 5862.
The arithmetic mean is 2931.

2 odd divisors

1, 5861

How to compute the divisors of 5861?

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 5861 by each of the numbers from 1 to 5861 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)

5861 / 1 = 5861 (the remainder is 0, so 1 is a divisor of 5861)
5861 / 2 = 2930.5 (the remainder is 1, so 2 is not a divisor of 5861)
5861 / 3 = 1953.6666666667 (the remainder is 2, so 3 is not a divisor of 5861)
...
5861 / 5860 = 1.0001706484642 (the remainder is 1, so 5860 is not a divisor of 5861)
5861 / 5861 = 1 (the remainder is 0, so 5861 is a divisor of 5861)

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 5861 (i.e. 76.557168181693). 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 $\frac{N}{d} = D$ )

5861 / 1 = 5861 (the remainder is 0, so 1 and 5861 are divisors of 5861)
5861 / 2 = 2930.5 (the remainder is 1, so 2 is not a divisor of 5861)
5861 / 3 = 1953.6666666667 (the remainder is 2, so 3 is not a divisor of 5861)
...
5861 / 75 = 78.146666666667 (the remainder is 11, so 75 is not a divisor of 5861)
5861 / 76 = 77.118421052632 (the remainder is 9, so 76 is not a divisor of 5861)