What are the divisors of 2313?

1, 3, 9, 257, 771, 2313

There is a total of 6 positive divisors.
The sum of these divisors is 3354.
The arithmetic mean is 559.

6 odd divisors

1, 3, 9, 257, 771, 2313

How to compute the divisors of 2313?

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 2313 by each of the numbers from 1 to 2313 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)

2313 / 1 = 2313 (the remainder is 0, so 1 is a divisor of 2313)
2313 / 2 = 1156.5 (the remainder is 1, so 2 is not a divisor of 2313)
2313 / 3 = 771 (the remainder is 0, so 3 is a divisor of 2313)
...
2313 / 2312 = 1.0004325259516 (the remainder is 1, so 2312 is not a divisor of 2313)
2313 / 2313 = 1 (the remainder is 0, so 2313 is a divisor of 2313)

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 2313 (i.e. 48.093658625644). 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 $\frac{N}{d} = D$ )

2313 / 1 = 2313 (the remainder is 0, so 1 and 2313 are divisors of 2313)
2313 / 2 = 1156.5 (the remainder is 1, so 2 is not a divisor of 2313)
2313 / 3 = 771 (the remainder is 0, so 3 and 771 are divisors of 2313)
...
2313 / 47 = 49.212765957447 (the remainder is 10, so 47 is not a divisor of 2313)
2313 / 48 = 48.1875 (the remainder is 9, so 48 is not a divisor of 2313)