What are the divisors of 5723?

1, 59, 97, 5723

There is a total of 4 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 1470.

4 odd divisors

1, 59, 97, 5723

How to compute the divisors of 5723?

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 5723 by each of the numbers from 1 to 5723 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)

5723 / 1 = 5723 (the remainder is 0, so 1 is a divisor of 5723)
5723 / 2 = 2861.5 (the remainder is 1, so 2 is not a divisor of 5723)
5723 / 3 = 1907.6666666667 (the remainder is 2, so 3 is not a divisor of 5723)
...
5723 / 5722 = 1.0001747640685 (the remainder is 1, so 5722 is not a divisor of 5723)
5723 / 5723 = 1 (the remainder is 0, so 5723 is a divisor of 5723)

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 5723 (i.e. 75.650512225629). 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 $\frac{N}{d} = D$ )

5723 / 1 = 5723 (the remainder is 0, so 1 and 5723 are divisors of 5723)
5723 / 2 = 2861.5 (the remainder is 1, so 2 is not a divisor of 5723)
5723 / 3 = 1907.6666666667 (the remainder is 2, so 3 is not a divisor of 5723)
...
5723 / 74 = 77.337837837838 (the remainder is 25, so 74 is not a divisor of 5723)
5723 / 75 = 76.306666666667 (the remainder is 23, so 75 is not a divisor of 5723)