What are the divisors of 3851?

1, 3851

There is a total of 2 positive divisors.
The sum of these divisors is 3852.
The arithmetic mean is 1926.

2 odd divisors

1, 3851

How to compute the divisors of 3851?

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 3851 by each of the numbers from 1 to 3851 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)

3851 / 1 = 3851 (the remainder is 0, so 1 is a divisor of 3851)
3851 / 2 = 1925.5 (the remainder is 1, so 2 is not a divisor of 3851)
3851 / 3 = 1283.6666666667 (the remainder is 2, so 3 is not a divisor of 3851)
...
3851 / 3850 = 1.0002597402597 (the remainder is 1, so 3850 is not a divisor of 3851)
3851 / 3851 = 1 (the remainder is 0, so 3851 is a divisor of 3851)

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 3851 (i.e. 62.056425936401). 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 $\frac{N}{d} = D$ )

3851 / 1 = 3851 (the remainder is 0, so 1 and 3851 are divisors of 3851)
3851 / 2 = 1925.5 (the remainder is 1, so 2 is not a divisor of 3851)
3851 / 3 = 1283.6666666667 (the remainder is 2, so 3 is not a divisor of 3851)
...
3851 / 61 = 63.131147540984 (the remainder is 8, so 61 is not a divisor of 3851)
3851 / 62 = 62.112903225806 (the remainder is 7, so 62 is not a divisor of 3851)