What are the divisors of 7085?

1, 5, 13, 65, 109, 545, 1417, 7085

There is a total of 8 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 1155.

8 odd divisors

1, 5, 13, 65, 109, 545, 1417, 7085

How to compute the divisors of 7085?

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 7085 by each of the numbers from 1 to 7085 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)

7085 / 1 = 7085 (the remainder is 0, so 1 is a divisor of 7085)
7085 / 2 = 3542.5 (the remainder is 1, so 2 is not a divisor of 7085)
7085 / 3 = 2361.6666666667 (the remainder is 2, so 3 is not a divisor of 7085)
...
7085 / 7084 = 1.0001411631846 (the remainder is 1, so 7084 is not a divisor of 7085)
7085 / 7085 = 1 (the remainder is 0, so 7085 is a divisor of 7085)

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 7085 (i.e. 84.172442046076). 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 $\frac{N}{d} = D$ )

7085 / 1 = 7085 (the remainder is 0, so 1 and 7085 are divisors of 7085)
7085 / 2 = 3542.5 (the remainder is 1, so 2 is not a divisor of 7085)
7085 / 3 = 2361.6666666667 (the remainder is 2, so 3 is not a divisor of 7085)
...
7085 / 83 = 85.361445783133 (the remainder is 30, so 83 is not a divisor of 7085)
7085 / 84 = 84.345238095238 (the remainder is 29, so 84 is not a divisor of 7085)