What are the divisors of 2358?

1, 2, 3, 6, 9, 18, 131, 262, 393, 786, 1179, 2358

There is a total of 12 positive divisors.
The sum of these divisors is 5148.
The arithmetic mean is 429.

6 even divisors

2, 6, 18, 262, 786, 2358

6 odd divisors

1, 3, 9, 131, 393, 1179

How to compute the divisors of 2358?

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 2358 by each of the numbers from 1 to 2358 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)

2358 / 1 = 2358 (the remainder is 0, so 1 is a divisor of 2358)
2358 / 2 = 1179 (the remainder is 0, so 2 is a divisor of 2358)
2358 / 3 = 786 (the remainder is 0, so 3 is a divisor of 2358)
...
2358 / 2357 = 1.0004242681375 (the remainder is 1, so 2357 is not a divisor of 2358)
2358 / 2358 = 1 (the remainder is 0, so 2358 is a divisor of 2358)

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 2358 (i.e. 48.559242168716). 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 $\frac{N}{d} = D$ )

2358 / 1 = 2358 (the remainder is 0, so 1 and 2358 are divisors of 2358)
2358 / 2 = 1179 (the remainder is 0, so 2 and 1179 are divisors of 2358)
2358 / 3 = 786 (the remainder is 0, so 3 and 786 are divisors of 2358)
...
2358 / 47 = 50.170212765957 (the remainder is 8, so 47 is not a divisor of 2358)
2358 / 48 = 49.125 (the remainder is 6, so 48 is not a divisor of 2358)