What are the divisors of 2389?

1, 2389

There is a total of 2 positive divisors.
The sum of these divisors is 2390.
The arithmetic mean is 1195.

2 odd divisors

1, 2389

How to compute the divisors of 2389?

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 2389 by each of the numbers from 1 to 2389 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)

2389 / 1 = 2389 (the remainder is 0, so 1 is a divisor of 2389)
2389 / 2 = 1194.5 (the remainder is 1, so 2 is not a divisor of 2389)
2389 / 3 = 796.33333333333 (the remainder is 1, so 3 is not a divisor of 2389)
...
2389 / 2388 = 1.000418760469 (the remainder is 1, so 2388 is not a divisor of 2389)
2389 / 2389 = 1 (the remainder is 0, so 2389 is a divisor of 2389)

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 2389 (i.e. 48.8773976394). 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 $\frac{N}{d} = D$ )

2389 / 1 = 2389 (the remainder is 0, so 1 and 2389 are divisors of 2389)
2389 / 2 = 1194.5 (the remainder is 1, so 2 is not a divisor of 2389)
2389 / 3 = 796.33333333333 (the remainder is 1, so 3 is not a divisor of 2389)
...
2389 / 47 = 50.829787234043 (the remainder is 39, so 47 is not a divisor of 2389)
2389 / 48 = 49.770833333333 (the remainder is 37, so 48 is not a divisor of 2389)