What are the divisors of 2322?

1, 2, 3, 6, 9, 18, 27, 43, 54, 86, 129, 258, 387, 774, 1161, 2322

There is a total of 16 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 330.

8 even divisors

2, 6, 18, 54, 86, 258, 774, 2322

8 odd divisors

1, 3, 9, 27, 43, 129, 387, 1161

How to compute the divisors of 2322?

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 2322 by each of the numbers from 1 to 2322 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)

2322 / 1 = 2322 (the remainder is 0, so 1 is a divisor of 2322)
2322 / 2 = 1161 (the remainder is 0, so 2 is a divisor of 2322)
2322 / 3 = 774 (the remainder is 0, so 3 is a divisor of 2322)
...
2322 / 2321 = 1.0004308487721 (the remainder is 1, so 2321 is not a divisor of 2322)
2322 / 2322 = 1 (the remainder is 0, so 2322 is a divisor of 2322)

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 2322 (i.e. 48.187135212627). 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 $\frac{N}{d} = D$ )

2322 / 1 = 2322 (the remainder is 0, so 1 and 2322 are divisors of 2322)
2322 / 2 = 1161 (the remainder is 0, so 2 and 1161 are divisors of 2322)
2322 / 3 = 774 (the remainder is 0, so 3 and 774 are divisors of 2322)
...
2322 / 47 = 49.404255319149 (the remainder is 19, so 47 is not a divisor of 2322)
2322 / 48 = 48.375 (the remainder is 18, so 48 is not a divisor of 2322)