What are the divisors of 2366?

1, 2, 7, 13, 14, 26, 91, 169, 182, 338, 1183, 2366

There is a total of 12 positive divisors.
The sum of these divisors is 4392.
The arithmetic mean is 366.

6 even divisors

2, 14, 26, 182, 338, 2366

6 odd divisors

1, 7, 13, 91, 169, 1183

How to compute the divisors of 2366?

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 2366 by each of the numbers from 1 to 2366 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)

2366 / 1 = 2366 (the remainder is 0, so 1 is a divisor of 2366)
2366 / 2 = 1183 (the remainder is 0, so 2 is a divisor of 2366)
2366 / 3 = 788.66666666667 (the remainder is 2, so 3 is not a divisor of 2366)
...
2366 / 2365 = 1.000422832981 (the remainder is 1, so 2365 is not a divisor of 2366)
2366 / 2366 = 1 (the remainder is 0, so 2366 is a divisor of 2366)

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 2366 (i.e. 48.641546028061). 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 $\frac{N}{d} = D$ )

2366 / 1 = 2366 (the remainder is 0, so 1 and 2366 are divisors of 2366)
2366 / 2 = 1183 (the remainder is 0, so 2 and 1183 are divisors of 2366)
2366 / 3 = 788.66666666667 (the remainder is 2, so 3 is not a divisor of 2366)
...
2366 / 47 = 50.340425531915 (the remainder is 16, so 47 is not a divisor of 2366)
2366 / 48 = 49.291666666667 (the remainder is 14, so 48 is not a divisor of 2366)