What are the divisors of 2329?

1, 17, 137, 2329

There is a total of 4 positive divisors.
The sum of these divisors is 2484.
The arithmetic mean is 621.

4 odd divisors

1, 17, 137, 2329

How to compute the divisors of 2329?

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 2329 by each of the numbers from 1 to 2329 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)

2329 / 1 = 2329 (the remainder is 0, so 1 is a divisor of 2329)
2329 / 2 = 1164.5 (the remainder is 1, so 2 is not a divisor of 2329)
2329 / 3 = 776.33333333333 (the remainder is 1, so 3 is not a divisor of 2329)
...
2329 / 2328 = 1.0004295532646 (the remainder is 1, so 2328 is not a divisor of 2329)
2329 / 2329 = 1 (the remainder is 0, so 2329 is a divisor of 2329)

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 2329 (i.e. 48.259714048055). 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 $\frac{N}{d} = D$ )

2329 / 1 = 2329 (the remainder is 0, so 1 and 2329 are divisors of 2329)
2329 / 2 = 1164.5 (the remainder is 1, so 2 is not a divisor of 2329)
2329 / 3 = 776.33333333333 (the remainder is 1, so 3 is not a divisor of 2329)
...
2329 / 47 = 49.553191489362 (the remainder is 26, so 47 is not a divisor of 2329)
2329 / 48 = 48.520833333333 (the remainder is 25, so 48 is not a divisor of 2329)