What are the divisors of 3895?

1, 5, 19, 41, 95, 205, 779, 3895

There is a total of 8 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 630.

8 odd divisors

1, 5, 19, 41, 95, 205, 779, 3895

How to compute the divisors of 3895?

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 3895 by each of the numbers from 1 to 3895 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)

3895 / 1 = 3895 (the remainder is 0, so 1 is a divisor of 3895)
3895 / 2 = 1947.5 (the remainder is 1, so 2 is not a divisor of 3895)
3895 / 3 = 1298.3333333333 (the remainder is 1, so 3 is not a divisor of 3895)
...
3895 / 3894 = 1.0002568053416 (the remainder is 1, so 3894 is not a divisor of 3895)
3895 / 3895 = 1 (the remainder is 0, so 3895 is a divisor of 3895)

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 3895 (i.e. 62.40993510652). 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 $\frac{N}{d} = D$ )

3895 / 1 = 3895 (the remainder is 0, so 1 and 3895 are divisors of 3895)
3895 / 2 = 1947.5 (the remainder is 1, so 2 is not a divisor of 3895)
3895 / 3 = 1298.3333333333 (the remainder is 1, so 3 is not a divisor of 3895)
...
3895 / 61 = 63.852459016393 (the remainder is 52, so 61 is not a divisor of 3895)
3895 / 62 = 62.822580645161 (the remainder is 51, so 62 is not a divisor of 3895)