What are the divisors of 9099?

1, 3, 9, 27, 337, 1011, 3033, 9099

There is a total of 8 positive divisors.
The sum of these divisors is 13520.
The arithmetic mean is 1690.

8 odd divisors

1, 3, 9, 27, 337, 1011, 3033, 9099

How to compute the divisors of 9099?

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 9099 by each of the numbers from 1 to 9099 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)

9099 / 1 = 9099 (the remainder is 0, so 1 is a divisor of 9099)
9099 / 2 = 4549.5 (the remainder is 1, so 2 is not a divisor of 9099)
9099 / 3 = 3033 (the remainder is 0, so 3 is a divisor of 9099)
...
9099 / 9098 = 1.0001099142669 (the remainder is 1, so 9098 is not a divisor of 9099)
9099 / 9099 = 1 (the remainder is 0, so 9099 is a divisor of 9099)

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 9099 (i.e. 95.388678573508). 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 $\frac{N}{d} = D$ )

9099 / 1 = 9099 (the remainder is 0, so 1 and 9099 are divisors of 9099)
9099 / 2 = 4549.5 (the remainder is 1, so 2 is not a divisor of 9099)
9099 / 3 = 3033 (the remainder is 0, so 3 and 3033 are divisors of 9099)
...
9099 / 94 = 96.797872340426 (the remainder is 75, so 94 is not a divisor of 9099)
9099 / 95 = 95.778947368421 (the remainder is 74, so 95 is not a divisor of 9099)