What are the divisors of 9200?

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 40, 46, 50, 80, 92, 100, 115, 184, 200, 230, 368, 400, 460, 575, 920, 1150, 1840, 2300, 4600, 9200

There is a total of 30 positive divisors.
The sum of these divisors is 23064.
The arithmetic mean is 768.8.

24 even divisors

2, 4, 8, 10, 16, 20, 40, 46, 50, 80, 92, 100, 184, 200, 230, 368, 400, 460, 920, 1150, 1840, 2300, 4600, 9200

6 odd divisors

1, 5, 23, 25, 115, 575

How to compute the divisors of 9200?

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 9200 by each of the numbers from 1 to 9200 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)

9200 / 1 = 9200 (the remainder is 0, so 1 is a divisor of 9200)
9200 / 2 = 4600 (the remainder is 0, so 2 is a divisor of 9200)
9200 / 3 = 3066.6666666667 (the remainder is 2, so 3 is not a divisor of 9200)
...
9200 / 9199 = 1.0001087074682 (the remainder is 1, so 9199 is not a divisor of 9200)
9200 / 9200 = 1 (the remainder is 0, so 9200 is a divisor of 9200)

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 9200 (i.e. 95.916630466254). 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 $\frac{N}{d} = D$ )

9200 / 1 = 9200 (the remainder is 0, so 1 and 9200 are divisors of 9200)
9200 / 2 = 4600 (the remainder is 0, so 2 and 4600 are divisors of 9200)
9200 / 3 = 3066.6666666667 (the remainder is 2, so 3 is not a divisor of 9200)
...
9200 / 94 = 97.872340425532 (the remainder is 82, so 94 is not a divisor of 9200)
9200 / 95 = 96.842105263158 (the remainder is 80, so 95 is not a divisor of 9200)