What are the divisors of 2331?

1, 3, 7, 9, 21, 37, 63, 111, 259, 333, 777, 2331

There is a total of 12 positive divisors.
The sum of these divisors is 3952.
The arithmetic mean is 329.33333333333.

12 odd divisors

1, 3, 7, 9, 21, 37, 63, 111, 259, 333, 777, 2331

How to compute the divisors of 2331?

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 2331 by each of the numbers from 1 to 2331 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)

2331 / 1 = 2331 (the remainder is 0, so 1 is a divisor of 2331)
2331 / 2 = 1165.5 (the remainder is 1, so 2 is not a divisor of 2331)
2331 / 3 = 777 (the remainder is 0, so 3 is a divisor of 2331)
...
2331 / 2330 = 1.0004291845494 (the remainder is 1, so 2330 is not a divisor of 2331)
2331 / 2331 = 1 (the remainder is 0, so 2331 is a divisor of 2331)

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 2331 (i.e. 48.280430818293). 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 $\frac{N}{d} = D$ )

2331 / 1 = 2331 (the remainder is 0, so 1 and 2331 are divisors of 2331)
2331 / 2 = 1165.5 (the remainder is 1, so 2 is not a divisor of 2331)
2331 / 3 = 777 (the remainder is 0, so 3 and 777 are divisors of 2331)
...
2331 / 47 = 49.595744680851 (the remainder is 28, so 47 is not a divisor of 2331)
2331 / 48 = 48.5625 (the remainder is 27, so 48 is not a divisor of 2331)