What are the divisors of 2321?

1, 11, 211, 2321

There is a total of 4 positive divisors.
The sum of these divisors is 2544.
The arithmetic mean is 636.

4 odd divisors

1, 11, 211, 2321

How to compute the divisors of 2321?

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 2321 by each of the numbers from 1 to 2321 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)

2321 / 1 = 2321 (the remainder is 0, so 1 is a divisor of 2321)
2321 / 2 = 1160.5 (the remainder is 1, so 2 is not a divisor of 2321)
2321 / 3 = 773.66666666667 (the remainder is 2, so 3 is not a divisor of 2321)
...
2321 / 2320 = 1.0004310344828 (the remainder is 1, so 2320 is not a divisor of 2321)
2321 / 2321 = 1 (the remainder is 0, so 2321 is a divisor of 2321)

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 2321 (i.e. 48.176757881784). 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 $\frac{N}{d} = D$ )

2321 / 1 = 2321 (the remainder is 0, so 1 and 2321 are divisors of 2321)
2321 / 2 = 1160.5 (the remainder is 1, so 2 is not a divisor of 2321)
2321 / 3 = 773.66666666667 (the remainder is 2, so 3 is not a divisor of 2321)
...
2321 / 47 = 49.382978723404 (the remainder is 18, so 47 is not a divisor of 2321)
2321 / 48 = 48.354166666667 (the remainder is 17, so 48 is not a divisor of 2321)