What are the divisors of 3858?

1, 2, 3, 6, 643, 1286, 1929, 3858

There is a total of 8 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 966.

4 even divisors

2, 6, 1286, 3858

4 odd divisors

1, 3, 643, 1929

How to compute the divisors of 3858?

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 3858 by each of the numbers from 1 to 3858 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)

3858 / 1 = 3858 (the remainder is 0, so 1 is a divisor of 3858)
3858 / 2 = 1929 (the remainder is 0, so 2 is a divisor of 3858)
3858 / 3 = 1286 (the remainder is 0, so 3 is a divisor of 3858)
...
3858 / 3857 = 1.0002592688618 (the remainder is 1, so 3857 is not a divisor of 3858)
3858 / 3858 = 1 (the remainder is 0, so 3858 is a divisor of 3858)

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 3858 (i.e. 62.112800613078). 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 $\frac{N}{d} = D$ )

3858 / 1 = 3858 (the remainder is 0, so 1 and 3858 are divisors of 3858)
3858 / 2 = 1929 (the remainder is 0, so 2 and 1929 are divisors of 3858)
3858 / 3 = 1286 (the remainder is 0, so 3 and 1286 are divisors of 3858)
...
3858 / 61 = 63.245901639344 (the remainder is 15, so 61 is not a divisor of 3858)
3858 / 62 = 62.225806451613 (the remainder is 14, so 62 is not a divisor of 3858)