What are the divisors of 1865?

1, 5, 373, 1865

There is a total of 4 positive divisors.
The sum of these divisors is 2244.
The arithmetic mean is 561.

4 odd divisors

1, 5, 373, 1865

How to compute the divisors of 1865?

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 1865 by each of the numbers from 1 to 1865 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)

1865 / 1 = 1865 (the remainder is 0, so 1 is a divisor of 1865)
1865 / 2 = 932.5 (the remainder is 1, so 2 is not a divisor of 1865)
1865 / 3 = 621.66666666667 (the remainder is 2, so 3 is not a divisor of 1865)
...
1865 / 1864 = 1.0005364806867 (the remainder is 1, so 1864 is not a divisor of 1865)
1865 / 1865 = 1 (the remainder is 0, so 1865 is a divisor of 1865)

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 1865 (i.e. 43.185645763378). 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 $\frac{N}{d} = D$ )

1865 / 1 = 1865 (the remainder is 0, so 1 and 1865 are divisors of 1865)
1865 / 2 = 932.5 (the remainder is 1, so 2 is not a divisor of 1865)
1865 / 3 = 621.66666666667 (the remainder is 2, so 3 is not a divisor of 1865)
...
1865 / 42 = 44.404761904762 (the remainder is 17, so 42 is not a divisor of 1865)
1865 / 43 = 43.372093023256 (the remainder is 16, so 43 is not a divisor of 1865)