What are the divisors of 5923?

1, 5923

There is a total of 2 positive divisors.
The sum of these divisors is 5924.
The arithmetic mean is 2962.

2 odd divisors

1, 5923

How to compute the divisors of 5923?

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 5923 by each of the numbers from 1 to 5923 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)

5923 / 1 = 5923 (the remainder is 0, so 1 is a divisor of 5923)
5923 / 2 = 2961.5 (the remainder is 1, so 2 is not a divisor of 5923)
5923 / 3 = 1974.3333333333 (the remainder is 1, so 3 is not a divisor of 5923)
...
5923 / 5922 = 1.000168861871 (the remainder is 1, so 5922 is not a divisor of 5923)
5923 / 5923 = 1 (the remainder is 0, so 5923 is a divisor of 5923)

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 5923 (i.e. 76.961029099149). 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 $\frac{N}{d} = D$ )

5923 / 1 = 5923 (the remainder is 0, so 1 and 5923 are divisors of 5923)
5923 / 2 = 2961.5 (the remainder is 1, so 2 is not a divisor of 5923)
5923 / 3 = 1974.3333333333 (the remainder is 1, so 3 is not a divisor of 5923)
...
5923 / 75 = 78.973333333333 (the remainder is 73, so 75 is not a divisor of 5923)
5923 / 76 = 77.934210526316 (the remainder is 71, so 76 is not a divisor of 5923)