What are the divisors of 8289?

1, 3, 9, 27, 307, 921, 2763, 8289

There is a total of 8 positive divisors.
The sum of these divisors is 12320.
The arithmetic mean is 1540.

8 odd divisors

1, 3, 9, 27, 307, 921, 2763, 8289

How to compute the divisors of 8289?

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 8289 by each of the numbers from 1 to 8289 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)

8289 / 1 = 8289 (the remainder is 0, so 1 is a divisor of 8289)
8289 / 2 = 4144.5 (the remainder is 1, so 2 is not a divisor of 8289)
8289 / 3 = 2763 (the remainder is 0, so 3 is a divisor of 8289)
...
8289 / 8288 = 1.0001206563707 (the remainder is 1, so 8288 is not a divisor of 8289)
8289 / 8289 = 1 (the remainder is 0, so 8289 is a divisor of 8289)

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 8289 (i.e. 91.043945432961). 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 $\frac{N}{d} = D$ )

8289 / 1 = 8289 (the remainder is 0, so 1 and 8289 are divisors of 8289)
8289 / 2 = 4144.5 (the remainder is 1, so 2 is not a divisor of 8289)
8289 / 3 = 2763 (the remainder is 0, so 3 and 2763 are divisors of 8289)
...
8289 / 90 = 92.1 (the remainder is 9, so 90 is not a divisor of 8289)
8289 / 91 = 91.087912087912 (the remainder is 8, so 91 is not a divisor of 8289)