What are the divisors of 3865?

1, 5, 773, 3865

There is a total of 4 positive divisors.
The sum of these divisors is 4644.
The arithmetic mean is 1161.

4 odd divisors

1, 5, 773, 3865

How to compute the divisors of 3865?

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 3865 by each of the numbers from 1 to 3865 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)

3865 / 1 = 3865 (the remainder is 0, so 1 is a divisor of 3865)
3865 / 2 = 1932.5 (the remainder is 1, so 2 is not a divisor of 3865)
3865 / 3 = 1288.3333333333 (the remainder is 1, so 3 is not a divisor of 3865)
...
3865 / 3864 = 1.0002587991718 (the remainder is 1, so 3864 is not a divisor of 3865)
3865 / 3865 = 1 (the remainder is 0, so 3865 is a divisor of 3865)

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 3865 (i.e. 62.169124169478). 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 $\frac{N}{d} = D$ )

3865 / 1 = 3865 (the remainder is 0, so 1 and 3865 are divisors of 3865)
3865 / 2 = 1932.5 (the remainder is 1, so 2 is not a divisor of 3865)
3865 / 3 = 1288.3333333333 (the remainder is 1, so 3 is not a divisor of 3865)
...
3865 / 61 = 63.360655737705 (the remainder is 22, so 61 is not a divisor of 3865)
3865 / 62 = 62.338709677419 (the remainder is 21, so 62 is not a divisor of 3865)