What are the divisors of 2357?

1, 2357

There is a total of 2 positive divisors.
The sum of these divisors is 2358.
The arithmetic mean is 1179.

2 odd divisors

1, 2357

How to compute the divisors of 2357?

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 2357 by each of the numbers from 1 to 2357 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)

2357 / 1 = 2357 (the remainder is 0, so 1 is a divisor of 2357)
2357 / 2 = 1178.5 (the remainder is 1, so 2 is not a divisor of 2357)
2357 / 3 = 785.66666666667 (the remainder is 2, so 3 is not a divisor of 2357)
...
2357 / 2356 = 1.0004244482173 (the remainder is 1, so 2356 is not a divisor of 2357)
2357 / 2357 = 1 (the remainder is 0, so 2357 is a divisor of 2357)

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 2357 (i.e. 48.548944375753). 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 $\frac{N}{d} = D$ )

2357 / 1 = 2357 (the remainder is 0, so 1 and 2357 are divisors of 2357)
2357 / 2 = 1178.5 (the remainder is 1, so 2 is not a divisor of 2357)
2357 / 3 = 785.66666666667 (the remainder is 2, so 3 is not a divisor of 2357)
...
2357 / 47 = 50.148936170213 (the remainder is 7, so 47 is not a divisor of 2357)
2357 / 48 = 49.104166666667 (the remainder is 5, so 48 is not a divisor of 2357)