What are the divisors of 2394?

1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 38, 42, 57, 63, 114, 126, 133, 171, 266, 342, 399, 798, 1197, 2394

There is a total of 24 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 260.

12 even divisors

2, 6, 14, 18, 38, 42, 114, 126, 266, 342, 798, 2394

12 odd divisors

1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197

How to compute the divisors of 2394?

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 2394 by each of the numbers from 1 to 2394 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)

2394 / 1 = 2394 (the remainder is 0, so 1 is a divisor of 2394)
2394 / 2 = 1197 (the remainder is 0, so 2 is a divisor of 2394)
2394 / 3 = 798 (the remainder is 0, so 3 is a divisor of 2394)
...
2394 / 2393 = 1.0004178854994 (the remainder is 1, so 2393 is not a divisor of 2394)
2394 / 2394 = 1 (the remainder is 0, so 2394 is a divisor of 2394)

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 2394 (i.e. 48.9285192909). 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 $\frac{N}{d} = D$ )

2394 / 1 = 2394 (the remainder is 0, so 1 and 2394 are divisors of 2394)
2394 / 2 = 1197 (the remainder is 0, so 2 and 1197 are divisors of 2394)
2394 / 3 = 798 (the remainder is 0, so 3 and 798 are divisors of 2394)
...
2394 / 47 = 50.936170212766 (the remainder is 44, so 47 is not a divisor of 2394)
2394 / 48 = 49.875 (the remainder is 42, so 48 is not a divisor of 2394)