What are the divisors of 2327?

1, 13, 179, 2327

There is a total of 4 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 630.

4 odd divisors

1, 13, 179, 2327

How to compute the divisors of 2327?

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 2327 by each of the numbers from 1 to 2327 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)

2327 / 1 = 2327 (the remainder is 0, so 1 is a divisor of 2327)
2327 / 2 = 1163.5 (the remainder is 1, so 2 is not a divisor of 2327)
2327 / 3 = 775.66666666667 (the remainder is 2, so 3 is not a divisor of 2327)
...
2327 / 2326 = 1.0004299226139 (the remainder is 1, so 2326 is not a divisor of 2327)
2327 / 2327 = 1 (the remainder is 0, so 2327 is a divisor of 2327)

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 2327 (i.e. 48.238988380769). 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 $\frac{N}{d} = D$ )

2327 / 1 = 2327 (the remainder is 0, so 1 and 2327 are divisors of 2327)
2327 / 2 = 1163.5 (the remainder is 1, so 2 is not a divisor of 2327)
2327 / 3 = 775.66666666667 (the remainder is 2, so 3 is not a divisor of 2327)
...
2327 / 47 = 49.510638297872 (the remainder is 24, so 47 is not a divisor of 2327)
2327 / 48 = 48.479166666667 (the remainder is 23, so 48 is not a divisor of 2327)