What are the divisors of 2334?

1, 2, 3, 6, 389, 778, 1167, 2334

There is a total of 8 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 585.

4 even divisors

2, 6, 778, 2334

4 odd divisors

1, 3, 389, 1167

How to compute the divisors of 2334?

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 2334 by each of the numbers from 1 to 2334 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)

2334 / 1 = 2334 (the remainder is 0, so 1 is a divisor of 2334)
2334 / 2 = 1167 (the remainder is 0, so 2 is a divisor of 2334)
2334 / 3 = 778 (the remainder is 0, so 3 is a divisor of 2334)
...
2334 / 2333 = 1.0004286326618 (the remainder is 1, so 2333 is not a divisor of 2334)
2334 / 2334 = 1 (the remainder is 0, so 2334 is a divisor of 2334)

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 2334 (i.e. 48.311489316725). 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 $\frac{N}{d} = D$ )

2334 / 1 = 2334 (the remainder is 0, so 1 and 2334 are divisors of 2334)
2334 / 2 = 1167 (the remainder is 0, so 2 and 1167 are divisors of 2334)
2334 / 3 = 778 (the remainder is 0, so 3 and 778 are divisors of 2334)
...
2334 / 47 = 49.659574468085 (the remainder is 31, so 47 is not a divisor of 2334)
2334 / 48 = 48.625 (the remainder is 30, so 48 is not a divisor of 2334)