What are the divisors of 2328?

1, 2, 3, 4, 6, 8, 12, 24, 97, 194, 291, 388, 582, 776, 1164, 2328

There is a total of 16 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 367.5.

12 even divisors

2, 4, 6, 8, 12, 24, 194, 388, 582, 776, 1164, 2328

4 odd divisors

1, 3, 97, 291

How to compute the divisors of 2328?

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 2328 by each of the numbers from 1 to 2328 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)

2328 / 1 = 2328 (the remainder is 0, so 1 is a divisor of 2328)
2328 / 2 = 1164 (the remainder is 0, so 2 is a divisor of 2328)
2328 / 3 = 776 (the remainder is 0, so 3 is a divisor of 2328)
...
2328 / 2327 = 1.0004297378599 (the remainder is 1, so 2327 is not a divisor of 2328)
2328 / 2328 = 1 (the remainder is 0, so 2328 is a divisor of 2328)

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 2328 (i.e. 48.249352327259). 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 $\frac{N}{d} = D$ )

2328 / 1 = 2328 (the remainder is 0, so 1 and 2328 are divisors of 2328)
2328 / 2 = 1164 (the remainder is 0, so 2 and 1164 are divisors of 2328)
2328 / 3 = 776 (the remainder is 0, so 3 and 776 are divisors of 2328)
...
2328 / 47 = 49.531914893617 (the remainder is 25, so 47 is not a divisor of 2328)
2328 / 48 = 48.5 (the remainder is 24, so 48 is not a divisor of 2328)