What are the divisors of 9093?

1, 3, 7, 21, 433, 1299, 3031, 9093

There is a total of 8 positive divisors.
The sum of these divisors is 13888.
The arithmetic mean is 1736.

8 odd divisors

1, 3, 7, 21, 433, 1299, 3031, 9093

How to compute the divisors of 9093?

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 9093 by each of the numbers from 1 to 9093 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)

9093 / 1 = 9093 (the remainder is 0, so 1 is a divisor of 9093)
9093 / 2 = 4546.5 (the remainder is 1, so 2 is not a divisor of 9093)
9093 / 3 = 3031 (the remainder is 0, so 3 is a divisor of 9093)
...
9093 / 9092 = 1.0001099868016 (the remainder is 1, so 9092 is not a divisor of 9093)
9093 / 9093 = 1 (the remainder is 0, so 9093 is a divisor of 9093)

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 9093 (i.e. 95.357223113931). 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 $\frac{N}{d} = D$ )

9093 / 1 = 9093 (the remainder is 0, so 1 and 9093 are divisors of 9093)
9093 / 2 = 4546.5 (the remainder is 1, so 2 is not a divisor of 9093)
9093 / 3 = 3031 (the remainder is 0, so 3 and 3031 are divisors of 9093)
...
9093 / 94 = 96.734042553191 (the remainder is 69, so 94 is not a divisor of 9093)
9093 / 95 = 95.715789473684 (the remainder is 68, so 95 is not a divisor of 9093)