What are the divisors of 2343?

1, 3, 11, 33, 71, 213, 781, 2343

There is a total of 8 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 432.

8 odd divisors

1, 3, 11, 33, 71, 213, 781, 2343

How to compute the divisors of 2343?

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 2343 by each of the numbers from 1 to 2343 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)

2343 / 1 = 2343 (the remainder is 0, so 1 is a divisor of 2343)
2343 / 2 = 1171.5 (the remainder is 1, so 2 is not a divisor of 2343)
2343 / 3 = 781 (the remainder is 0, so 3 is a divisor of 2343)
...
2343 / 2342 = 1.0004269854825 (the remainder is 1, so 2342 is not a divisor of 2343)
2343 / 2343 = 1 (the remainder is 0, so 2343 is a divisor of 2343)

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 2343 (i.e. 48.404545241124). 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 $\frac{N}{d} = D$ )

2343 / 1 = 2343 (the remainder is 0, so 1 and 2343 are divisors of 2343)
2343 / 2 = 1171.5 (the remainder is 1, so 2 is not a divisor of 2343)
2343 / 3 = 781 (the remainder is 0, so 3 and 781 are divisors of 2343)
...
2343 / 47 = 49.851063829787 (the remainder is 40, so 47 is not a divisor of 2343)
2343 / 48 = 48.8125 (the remainder is 39, so 48 is not a divisor of 2343)