What are the divisors of 5873?

1, 7, 839, 5873

There is a total of 4 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 1680.

4 odd divisors

1, 7, 839, 5873

How to compute the divisors of 5873?

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 5873 by each of the numbers from 1 to 5873 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)

5873 / 1 = 5873 (the remainder is 0, so 1 is a divisor of 5873)
5873 / 2 = 2936.5 (the remainder is 1, so 2 is not a divisor of 5873)
5873 / 3 = 1957.6666666667 (the remainder is 2, so 3 is not a divisor of 5873)
...
5873 / 5872 = 1.0001702997275 (the remainder is 1, so 5872 is not a divisor of 5873)
5873 / 5873 = 1 (the remainder is 0, so 5873 is a divisor of 5873)

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 5873 (i.e. 76.635500911784). 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 $\frac{N}{d} = D$ )

5873 / 1 = 5873 (the remainder is 0, so 1 and 5873 are divisors of 5873)
5873 / 2 = 2936.5 (the remainder is 1, so 2 is not a divisor of 5873)
5873 / 3 = 1957.6666666667 (the remainder is 2, so 3 is not a divisor of 5873)
...
5873 / 75 = 78.306666666667 (the remainder is 23, so 75 is not a divisor of 5873)
5873 / 76 = 77.276315789474 (the remainder is 21, so 76 is not a divisor of 5873)