What are the divisors of 2356?

1, 2, 4, 19, 31, 38, 62, 76, 124, 589, 1178, 2356

There is a total of 12 positive divisors.
The sum of these divisors is 4480.
The arithmetic mean is 373.33333333333.

8 even divisors

2, 4, 38, 62, 76, 124, 1178, 2356

4 odd divisors

1, 19, 31, 589

How to compute the divisors of 2356?

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 2356 by each of the numbers from 1 to 2356 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)

2356 / 1 = 2356 (the remainder is 0, so 1 is a divisor of 2356)
2356 / 2 = 1178 (the remainder is 0, so 2 is a divisor of 2356)
2356 / 3 = 785.33333333333 (the remainder is 1, so 3 is not a divisor of 2356)
...
2356 / 2355 = 1.0004246284501 (the remainder is 1, so 2355 is not a divisor of 2356)
2356 / 2356 = 1 (the remainder is 0, so 2356 is a divisor of 2356)

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 2356 (i.e. 48.538644398046). 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 $\frac{N}{d} = D$ )

2356 / 1 = 2356 (the remainder is 0, so 1 and 2356 are divisors of 2356)
2356 / 2 = 1178 (the remainder is 0, so 2 and 1178 are divisors of 2356)
2356 / 3 = 785.33333333333 (the remainder is 1, so 3 is not a divisor of 2356)
...
2356 / 47 = 50.127659574468 (the remainder is 6, so 47 is not a divisor of 2356)
2356 / 48 = 49.083333333333 (the remainder is 4, so 48 is not a divisor of 2356)