What are the divisors of 8285?

1, 5, 1657, 8285

There is a total of 4 positive divisors.
The sum of these divisors is 9948.
The arithmetic mean is 2487.

4 odd divisors

1, 5, 1657, 8285

How to compute the divisors of 8285?

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 8285 by each of the numbers from 1 to 8285 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)

8285 / 1 = 8285 (the remainder is 0, so 1 is a divisor of 8285)
8285 / 2 = 4142.5 (the remainder is 1, so 2 is not a divisor of 8285)
8285 / 3 = 2761.6666666667 (the remainder is 2, so 3 is not a divisor of 8285)
...
8285 / 8284 = 1.0001207146306 (the remainder is 1, so 8284 is not a divisor of 8285)
8285 / 8285 = 1 (the remainder is 0, so 8285 is a divisor of 8285)

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 8285 (i.e. 91.021975368589). 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 $\frac{N}{d} = D$ )

8285 / 1 = 8285 (the remainder is 0, so 1 and 8285 are divisors of 8285)
8285 / 2 = 4142.5 (the remainder is 1, so 2 is not a divisor of 8285)
8285 / 3 = 2761.6666666667 (the remainder is 2, so 3 is not a divisor of 8285)
...
8285 / 90 = 92.055555555556 (the remainder is 5, so 90 is not a divisor of 8285)
8285 / 91 = 91.043956043956 (the remainder is 4, so 91 is not a divisor of 8285)