What are the divisors of 8089?

1, 8089

There is a total of 2 positive divisors.
The sum of these divisors is 8090.
The arithmetic mean is 4045.

2 odd divisors

1, 8089

How to compute the divisors of 8089?

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 8089 by each of the numbers from 1 to 8089 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)

8089 / 1 = 8089 (the remainder is 0, so 1 is a divisor of 8089)
8089 / 2 = 4044.5 (the remainder is 1, so 2 is not a divisor of 8089)
8089 / 3 = 2696.3333333333 (the remainder is 1, so 3 is not a divisor of 8089)
...
8089 / 8088 = 1.0001236399604 (the remainder is 1, so 8088 is not a divisor of 8089)
8089 / 8089 = 1 (the remainder is 0, so 8089 is a divisor of 8089)

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 8089 (i.e. 89.93886812719). 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 $\frac{N}{d} = D$ )

8089 / 1 = 8089 (the remainder is 0, so 1 and 8089 are divisors of 8089)
8089 / 2 = 4044.5 (the remainder is 1, so 2 is not a divisor of 8089)
8089 / 3 = 2696.3333333333 (the remainder is 1, so 3 is not a divisor of 8089)
...
8089 / 88 = 91.920454545455 (the remainder is 81, so 88 is not a divisor of 8089)
8089 / 89 = 90.887640449438 (the remainder is 79, so 89 is not a divisor of 8089)