What are the divisors of 9208?

1, 2, 4, 8, 1151, 2302, 4604, 9208

There is a total of 8 positive divisors.
The sum of these divisors is 17280.
The arithmetic mean is 2160.

6 even divisors

2, 4, 8, 2302, 4604, 9208

2 odd divisors

1, 1151

How to compute the divisors of 9208?

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 9208 by each of the numbers from 1 to 9208 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)

9208 / 1 = 9208 (the remainder is 0, so 1 is a divisor of 9208)
9208 / 2 = 4604 (the remainder is 0, so 2 is a divisor of 9208)
9208 / 3 = 3069.3333333333 (the remainder is 1, so 3 is not a divisor of 9208)
...
9208 / 9207 = 1.0001086130118 (the remainder is 1, so 9207 is not a divisor of 9208)
9208 / 9208 = 1 (the remainder is 0, so 9208 is a divisor of 9208)

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 9208 (i.e. 95.958324287161). 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 $\frac{N}{d} = D$ )

9208 / 1 = 9208 (the remainder is 0, so 1 and 9208 are divisors of 9208)
9208 / 2 = 4604 (the remainder is 0, so 2 and 4604 are divisors of 9208)
9208 / 3 = 3069.3333333333 (the remainder is 1, so 3 is not a divisor of 9208)
...
9208 / 94 = 97.957446808511 (the remainder is 90, so 94 is not a divisor of 9208)
9208 / 95 = 96.926315789474 (the remainder is 88, so 95 is not a divisor of 9208)