What are the divisors of 3859?

1, 17, 227, 3859

There is a total of 4 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 1026.

4 odd divisors

1, 17, 227, 3859

How to compute the divisors of 3859?

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 3859 by each of the numbers from 1 to 3859 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)

3859 / 1 = 3859 (the remainder is 0, so 1 is a divisor of 3859)
3859 / 2 = 1929.5 (the remainder is 1, so 2 is not a divisor of 3859)
3859 / 3 = 1286.3333333333 (the remainder is 1, so 3 is not a divisor of 3859)
...
3859 / 3858 = 1.0002592016589 (the remainder is 1, so 3858 is not a divisor of 3859)
3859 / 3859 = 1 (the remainder is 0, so 3859 is a divisor of 3859)

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 3859 (i.e. 62.120849961989). 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 $\frac{N}{d} = D$ )

3859 / 1 = 3859 (the remainder is 0, so 1 and 3859 are divisors of 3859)
3859 / 2 = 1929.5 (the remainder is 1, so 2 is not a divisor of 3859)
3859 / 3 = 1286.3333333333 (the remainder is 1, so 3 is not a divisor of 3859)
...
3859 / 61 = 63.262295081967 (the remainder is 16, so 61 is not a divisor of 3859)
3859 / 62 = 62.241935483871 (the remainder is 15, so 62 is not a divisor of 3859)