What are the divisors of 8185?

1, 5, 1637, 8185

There is a total of 4 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 2457.

4 odd divisors

1, 5, 1637, 8185

How to compute the divisors of 8185?

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 8185 by each of the numbers from 1 to 8185 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)

8185 / 1 = 8185 (the remainder is 0, so 1 is a divisor of 8185)
8185 / 2 = 4092.5 (the remainder is 1, so 2 is not a divisor of 8185)
8185 / 3 = 2728.3333333333 (the remainder is 1, so 3 is not a divisor of 8185)
...
8185 / 8184 = 1.0001221896383 (the remainder is 1, so 8184 is not a divisor of 8185)
8185 / 8185 = 1 (the remainder is 0, so 8185 is a divisor of 8185)

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 8185 (i.e. 90.470989825468). 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 $\frac{N}{d} = D$ )

8185 / 1 = 8185 (the remainder is 0, so 1 and 8185 are divisors of 8185)
8185 / 2 = 4092.5 (the remainder is 1, so 2 is not a divisor of 8185)
8185 / 3 = 2728.3333333333 (the remainder is 1, so 3 is not a divisor of 8185)
...
8185 / 89 = 91.966292134831 (the remainder is 86, so 89 is not a divisor of 8185)
8185 / 90 = 90.944444444444 (the remainder is 85, so 90 is not a divisor of 8185)