What are the divisors of 3085?

1, 5, 617, 3085

There is a total of 4 positive divisors.
The sum of these divisors is 3708.
The arithmetic mean is 927.

4 odd divisors

1, 5, 617, 3085

How to compute the divisors of 3085?

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 3085 by each of the numbers from 1 to 3085 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)

3085 / 1 = 3085 (the remainder is 0, so 1 is a divisor of 3085)
3085 / 2 = 1542.5 (the remainder is 1, so 2 is not a divisor of 3085)
3085 / 3 = 1028.3333333333 (the remainder is 1, so 3 is not a divisor of 3085)
...
3085 / 3084 = 1.0003242542153 (the remainder is 1, so 3084 is not a divisor of 3085)
3085 / 3085 = 1 (the remainder is 0, so 3085 is a divisor of 3085)

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 3085 (i.e. 55.542776307995). 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 $\frac{N}{d} = D$ )

3085 / 1 = 3085 (the remainder is 0, so 1 and 3085 are divisors of 3085)
3085 / 2 = 1542.5 (the remainder is 1, so 2 is not a divisor of 3085)
3085 / 3 = 1028.3333333333 (the remainder is 1, so 3 is not a divisor of 3085)
...
3085 / 54 = 57.12962962963 (the remainder is 7, so 54 is not a divisor of 3085)
3085 / 55 = 56.090909090909 (the remainder is 5, so 55 is not a divisor of 3085)