What are the divisors of 8200?

1, 2, 4, 5, 8, 10, 20, 25, 40, 41, 50, 82, 100, 164, 200, 205, 328, 410, 820, 1025, 1640, 2050, 4100, 8200

There is a total of 24 positive divisors.
The sum of these divisors is 19530.
The arithmetic mean is 813.75.

18 even divisors

2, 4, 8, 10, 20, 40, 50, 82, 100, 164, 200, 328, 410, 820, 1640, 2050, 4100, 8200

6 odd divisors

1, 5, 25, 41, 205, 1025

How to compute the divisors of 8200?

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 8200 by each of the numbers from 1 to 8200 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)

8200 / 1 = 8200 (the remainder is 0, so 1 is a divisor of 8200)
8200 / 2 = 4100 (the remainder is 0, so 2 is a divisor of 8200)
8200 / 3 = 2733.3333333333 (the remainder is 1, so 3 is not a divisor of 8200)
...
8200 / 8199 = 1.0001219660934 (the remainder is 1, so 8199 is not a divisor of 8200)
8200 / 8200 = 1 (the remainder is 0, so 8200 is a divisor of 8200)

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 8200 (i.e. 90.553851381374). 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 $\frac{N}{d} = D$ )

8200 / 1 = 8200 (the remainder is 0, so 1 and 8200 are divisors of 8200)
8200 / 2 = 4100 (the remainder is 0, so 2 and 4100 are divisors of 8200)
8200 / 3 = 2733.3333333333 (the remainder is 1, so 3 is not a divisor of 8200)
...
8200 / 89 = 92.134831460674 (the remainder is 12, so 89 is not a divisor of 8200)
8200 / 90 = 91.111111111111 (the remainder is 10, so 90 is not a divisor of 8200)