What are the divisors of 2365?

1, 5, 11, 43, 55, 215, 473, 2365

There is a total of 8 positive divisors.
The sum of these divisors is 3168.
The arithmetic mean is 396.

8 odd divisors

1, 5, 11, 43, 55, 215, 473, 2365

How to compute the divisors of 2365?

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 2365 by each of the numbers from 1 to 2365 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)

2365 / 1 = 2365 (the remainder is 0, so 1 is a divisor of 2365)
2365 / 2 = 1182.5 (the remainder is 1, so 2 is not a divisor of 2365)
2365 / 3 = 788.33333333333 (the remainder is 1, so 3 is not a divisor of 2365)
...
2365 / 2364 = 1.0004230118443 (the remainder is 1, so 2364 is not a divisor of 2365)
2365 / 2365 = 1 (the remainder is 0, so 2365 is a divisor of 2365)

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 2365 (i.e. 48.631265663151). 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 $\frac{N}{d} = D$ )

2365 / 1 = 2365 (the remainder is 0, so 1 and 2365 are divisors of 2365)
2365 / 2 = 1182.5 (the remainder is 1, so 2 is not a divisor of 2365)
2365 / 3 = 788.33333333333 (the remainder is 1, so 3 is not a divisor of 2365)
...
2365 / 47 = 50.31914893617 (the remainder is 15, so 47 is not a divisor of 2365)
2365 / 48 = 49.270833333333 (the remainder is 13, so 48 is not a divisor of 2365)