What are the divisors of 2359?

1, 7, 337, 2359

There is a total of 4 positive divisors.
The sum of these divisors is 2704.
The arithmetic mean is 676.

4 odd divisors

1, 7, 337, 2359

How to compute the divisors of 2359?

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 2359 by each of the numbers from 1 to 2359 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)

2359 / 1 = 2359 (the remainder is 0, so 1 is a divisor of 2359)
2359 / 2 = 1179.5 (the remainder is 1, so 2 is not a divisor of 2359)
2359 / 3 = 786.33333333333 (the remainder is 1, so 3 is not a divisor of 2359)
...
2359 / 2358 = 1.0004240882103 (the remainder is 1, so 2358 is not a divisor of 2359)
2359 / 2359 = 1 (the remainder is 0, so 2359 is a divisor of 2359)

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 2359 (i.e. 48.569537778324). 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 $\frac{N}{d} = D$ )

2359 / 1 = 2359 (the remainder is 0, so 1 and 2359 are divisors of 2359)
2359 / 2 = 1179.5 (the remainder is 1, so 2 is not a divisor of 2359)
2359 / 3 = 786.33333333333 (the remainder is 1, so 3 is not a divisor of 2359)
...
2359 / 47 = 50.191489361702 (the remainder is 9, so 47 is not a divisor of 2359)
2359 / 48 = 49.145833333333 (the remainder is 7, so 48 is not a divisor of 2359)