What are the divisors of 2369?

1, 23, 103, 2369

There is a total of 4 positive divisors.
The sum of these divisors is 2496.
The arithmetic mean is 624.

4 odd divisors

1, 23, 103, 2369

How to compute the divisors of 2369?

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 2369 by each of the numbers from 1 to 2369 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)

2369 / 1 = 2369 (the remainder is 0, so 1 is a divisor of 2369)
2369 / 2 = 1184.5 (the remainder is 1, so 2 is not a divisor of 2369)
2369 / 3 = 789.66666666667 (the remainder is 2, so 3 is not a divisor of 2369)
...
2369 / 2368 = 1.0004222972973 (the remainder is 1, so 2368 is not a divisor of 2369)
2369 / 2369 = 1 (the remainder is 0, so 2369 is a divisor of 2369)

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 2369 (i.e. 48.672374094552). 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 $\frac{N}{d} = D$ )

2369 / 1 = 2369 (the remainder is 0, so 1 and 2369 are divisors of 2369)
2369 / 2 = 1184.5 (the remainder is 1, so 2 is not a divisor of 2369)
2369 / 3 = 789.66666666667 (the remainder is 2, so 3 is not a divisor of 2369)
...
2369 / 47 = 50.404255319149 (the remainder is 19, so 47 is not a divisor of 2369)
2369 / 48 = 49.354166666667 (the remainder is 17, so 48 is not a divisor of 2369)