What are the divisors of 2395?

1, 5, 479, 2395

There is a total of 4 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 720.

4 odd divisors

1, 5, 479, 2395

How to compute the divisors of 2395?

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 2395 by each of the numbers from 1 to 2395 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)

2395 / 1 = 2395 (the remainder is 0, so 1 is a divisor of 2395)
2395 / 2 = 1197.5 (the remainder is 1, so 2 is not a divisor of 2395)
2395 / 3 = 798.33333333333 (the remainder is 1, so 3 is not a divisor of 2395)
...
2395 / 2394 = 1.000417710944 (the remainder is 1, so 2394 is not a divisor of 2395)
2395 / 2395 = 1 (the remainder is 0, so 2395 is a divisor of 2395)

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 2395 (i.e. 48.938737212969). 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 $\frac{N}{d} = D$ )

2395 / 1 = 2395 (the remainder is 0, so 1 and 2395 are divisors of 2395)
2395 / 2 = 1197.5 (the remainder is 1, so 2 is not a divisor of 2395)
2395 / 3 = 798.33333333333 (the remainder is 1, so 3 is not a divisor of 2395)
...
2395 / 47 = 50.957446808511 (the remainder is 45, so 47 is not a divisor of 2395)
2395 / 48 = 49.895833333333 (the remainder is 43, so 48 is not a divisor of 2395)