What are the divisors of 8300?

1, 2, 4, 5, 10, 20, 25, 50, 83, 100, 166, 332, 415, 830, 1660, 2075, 4150, 8300

There is a total of 18 positive divisors.
The sum of these divisors is 18228.
The arithmetic mean is 1012.6666666667.

12 even divisors

2, 4, 10, 20, 50, 100, 166, 332, 830, 1660, 4150, 8300

6 odd divisors

1, 5, 25, 83, 415, 2075

How to compute the divisors of 8300?

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 8300 by each of the numbers from 1 to 8300 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)

8300 / 1 = 8300 (the remainder is 0, so 1 is a divisor of 8300)
8300 / 2 = 4150 (the remainder is 0, so 2 is a divisor of 8300)
8300 / 3 = 2766.6666666667 (the remainder is 2, so 3 is not a divisor of 8300)
...
8300 / 8299 = 1.0001204964454 (the remainder is 1, so 8299 is not a divisor of 8300)
8300 / 8300 = 1 (the remainder is 0, so 8300 is a divisor of 8300)

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 8300 (i.e. 91.104335791443). 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 $\frac{N}{d} = D$ )

8300 / 1 = 8300 (the remainder is 0, so 1 and 8300 are divisors of 8300)
8300 / 2 = 4150 (the remainder is 0, so 2 and 4150 are divisors of 8300)
8300 / 3 = 2766.6666666667 (the remainder is 2, so 3 is not a divisor of 8300)
...
8300 / 90 = 92.222222222222 (the remainder is 20, so 90 is not a divisor of 8300)
8300 / 91 = 91.208791208791 (the remainder is 19, so 91 is not a divisor of 8300)