What are the divisors of 2314?

1, 2, 13, 26, 89, 178, 1157, 2314

There is a total of 8 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 472.5.

4 even divisors

2, 26, 178, 2314

4 odd divisors

1, 13, 89, 1157

How to compute the divisors of 2314?

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 2314 by each of the numbers from 1 to 2314 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)

2314 / 1 = 2314 (the remainder is 0, so 1 is a divisor of 2314)
2314 / 2 = 1157 (the remainder is 0, so 2 is a divisor of 2314)
2314 / 3 = 771.33333333333 (the remainder is 1, so 3 is not a divisor of 2314)
...
2314 / 2313 = 1.0004323389537 (the remainder is 1, so 2313 is not a divisor of 2314)
2314 / 2314 = 1 (the remainder is 0, so 2314 is a divisor of 2314)

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 2314 (i.e. 48.104053883223). 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 $\frac{N}{d} = D$ )

2314 / 1 = 2314 (the remainder is 0, so 1 and 2314 are divisors of 2314)
2314 / 2 = 1157 (the remainder is 0, so 2 and 1157 are divisors of 2314)
2314 / 3 = 771.33333333333 (the remainder is 1, so 3 is not a divisor of 2314)
...
2314 / 47 = 49.234042553191 (the remainder is 11, so 47 is not a divisor of 2314)
2314 / 48 = 48.208333333333 (the remainder is 10, so 48 is not a divisor of 2314)