What are the divisors of 8150?

1, 2, 5, 10, 25, 50, 163, 326, 815, 1630, 4075, 8150

There is a total of 12 positive divisors.
The sum of these divisors is 15252.
The arithmetic mean is 1271.

6 even divisors

2, 10, 50, 326, 1630, 8150

6 odd divisors

1, 5, 25, 163, 815, 4075

How to compute the divisors of 8150?

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 8150 by each of the numbers from 1 to 8150 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)

8150 / 1 = 8150 (the remainder is 0, so 1 is a divisor of 8150)
8150 / 2 = 4075 (the remainder is 0, so 2 is a divisor of 8150)
8150 / 3 = 2716.6666666667 (the remainder is 2, so 3 is not a divisor of 8150)
...
8150 / 8149 = 1.0001227144435 (the remainder is 1, so 8149 is not a divisor of 8150)
8150 / 8150 = 1 (the remainder is 0, so 8150 is a divisor of 8150)

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 8150 (i.e. 90.277350426339). 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 $\frac{N}{d} = D$ )

8150 / 1 = 8150 (the remainder is 0, so 1 and 8150 are divisors of 8150)
8150 / 2 = 4075 (the remainder is 0, so 2 and 4075 are divisors of 8150)
8150 / 3 = 2716.6666666667 (the remainder is 2, so 3 is not a divisor of 8150)
...
8150 / 89 = 91.573033707865 (the remainder is 51, so 89 is not a divisor of 8150)
8150 / 90 = 90.555555555556 (the remainder is 50, so 90 is not a divisor of 8150)