What are the divisors of 2383?

1, 2383

There is a total of 2 positive divisors.
The sum of these divisors is 2384.
The arithmetic mean is 1192.

2 odd divisors

1, 2383

How to compute the divisors of 2383?

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 2383 by each of the numbers from 1 to 2383 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)

2383 / 1 = 2383 (the remainder is 0, so 1 is a divisor of 2383)
2383 / 2 = 1191.5 (the remainder is 1, so 2 is not a divisor of 2383)
2383 / 3 = 794.33333333333 (the remainder is 1, so 3 is not a divisor of 2383)
...
2383 / 2382 = 1.0004198152813 (the remainder is 1, so 2382 is not a divisor of 2383)
2383 / 2383 = 1 (the remainder is 0, so 2383 is a divisor of 2383)

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 2383 (i.e. 48.815980989836). 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 $\frac{N}{d} = D$ )

2383 / 1 = 2383 (the remainder is 0, so 1 and 2383 are divisors of 2383)
2383 / 2 = 1191.5 (the remainder is 1, so 2 is not a divisor of 2383)
2383 / 3 = 794.33333333333 (the remainder is 1, so 3 is not a divisor of 2383)
...
2383 / 47 = 50.702127659574 (the remainder is 33, so 47 is not a divisor of 2383)
2383 / 48 = 49.645833333333 (the remainder is 31, so 48 is not a divisor of 2383)