What are the divisors of 8245?

1, 5, 17, 85, 97, 485, 1649, 8245

There is a total of 8 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 1323.

8 odd divisors

1, 5, 17, 85, 97, 485, 1649, 8245

How to compute the divisors of 8245?

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 8245 by each of the numbers from 1 to 8245 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)

8245 / 1 = 8245 (the remainder is 0, so 1 is a divisor of 8245)
8245 / 2 = 4122.5 (the remainder is 1, so 2 is not a divisor of 8245)
8245 / 3 = 2748.3333333333 (the remainder is 1, so 3 is not a divisor of 8245)
...
8245 / 8244 = 1.0001213003396 (the remainder is 1, so 8244 is not a divisor of 8245)
8245 / 8245 = 1 (the remainder is 0, so 8245 is a divisor of 8245)

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 8245 (i.e. 90.801982357215). 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 $\frac{N}{d} = D$ )

8245 / 1 = 8245 (the remainder is 0, so 1 and 8245 are divisors of 8245)
8245 / 2 = 4122.5 (the remainder is 1, so 2 is not a divisor of 8245)
8245 / 3 = 2748.3333333333 (the remainder is 1, so 3 is not a divisor of 8245)
...
8245 / 89 = 92.640449438202 (the remainder is 57, so 89 is not a divisor of 8245)
8245 / 90 = 91.611111111111 (the remainder is 55, so 90 is not a divisor of 8245)