What are the divisors of 2326?

1, 2, 1163, 2326

There is a total of 4 positive divisors.
The sum of these divisors is 3492.
The arithmetic mean is 873.

2 even divisors

2, 2326

2 odd divisors

1, 1163

How to compute the divisors of 2326?

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 2326 by each of the numbers from 1 to 2326 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)

2326 / 1 = 2326 (the remainder is 0, so 1 is a divisor of 2326)
2326 / 2 = 1163 (the remainder is 0, so 2 is a divisor of 2326)
2326 / 3 = 775.33333333333 (the remainder is 1, so 3 is not a divisor of 2326)
...
2326 / 2325 = 1.0004301075269 (the remainder is 1, so 2325 is not a divisor of 2326)
2326 / 2326 = 1 (the remainder is 0, so 2326 is a divisor of 2326)

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 2326 (i.e. 48.22862220715). 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 $\frac{N}{d} = D$ )

2326 / 1 = 2326 (the remainder is 0, so 1 and 2326 are divisors of 2326)
2326 / 2 = 1163 (the remainder is 0, so 2 and 1163 are divisors of 2326)
2326 / 3 = 775.33333333333 (the remainder is 1, so 3 is not a divisor of 2326)
...
2326 / 47 = 49.489361702128 (the remainder is 23, so 47 is not a divisor of 2326)
2326 / 48 = 48.458333333333 (the remainder is 22, so 48 is not a divisor of 2326)