What are the divisors of 2393?

1, 2393

There is a total of 2 positive divisors.
The sum of these divisors is 2394.
The arithmetic mean is 1197.

2 odd divisors

1, 2393

How to compute the divisors of 2393?

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 2393 by each of the numbers from 1 to 2393 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)

2393 / 1 = 2393 (the remainder is 0, so 1 is a divisor of 2393)
2393 / 2 = 1196.5 (the remainder is 1, so 2 is not a divisor of 2393)
2393 / 3 = 797.66666666667 (the remainder is 2, so 3 is not a divisor of 2393)
...
2393 / 2392 = 1.0004180602007 (the remainder is 1, so 2392 is not a divisor of 2393)
2393 / 2393 = 1 (the remainder is 0, so 2393 is a divisor of 2393)

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 2393 (i.e. 48.91829923454). 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 $\frac{N}{d} = D$ )

2393 / 1 = 2393 (the remainder is 0, so 1 and 2393 are divisors of 2393)
2393 / 2 = 1196.5 (the remainder is 1, so 2 is not a divisor of 2393)
2393 / 3 = 797.66666666667 (the remainder is 2, so 3 is not a divisor of 2393)
...
2393 / 47 = 50.914893617021 (the remainder is 43, so 47 is not a divisor of 2393)
2393 / 48 = 49.854166666667 (the remainder is 41, so 48 is not a divisor of 2393)