What are the divisors of 3845?

1, 5, 769, 3845

There is a total of 4 positive divisors.
The sum of these divisors is 4620.
The arithmetic mean is 1155.

4 odd divisors

1, 5, 769, 3845

How to compute the divisors of 3845?

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 3845 by each of the numbers from 1 to 3845 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)

3845 / 1 = 3845 (the remainder is 0, so 1 is a divisor of 3845)
3845 / 2 = 1922.5 (the remainder is 1, so 2 is not a divisor of 3845)
3845 / 3 = 1281.6666666667 (the remainder is 2, so 3 is not a divisor of 3845)
...
3845 / 3844 = 1.0002601456816 (the remainder is 1, so 3844 is not a divisor of 3845)
3845 / 3845 = 1 (the remainder is 0, so 3845 is a divisor of 3845)

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 3845 (i.e. 62.00806399171). 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 $\frac{N}{d} = D$ )

3845 / 1 = 3845 (the remainder is 0, so 1 and 3845 are divisors of 3845)
3845 / 2 = 1922.5 (the remainder is 1, so 2 is not a divisor of 3845)
3845 / 3 = 1281.6666666667 (the remainder is 2, so 3 is not a divisor of 3845)
...
3845 / 61 = 63.032786885246 (the remainder is 2, so 61 is not a divisor of 3845)
3845 / 62 = 62.016129032258 (the remainder is 1, so 62 is not a divisor of 3845)