What are the divisors of 8099?

1, 7, 13, 89, 91, 623, 1157, 8099

There is a total of 8 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 1260.

8 odd divisors

1, 7, 13, 89, 91, 623, 1157, 8099

How to compute the divisors of 8099?

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 8099 by each of the numbers from 1 to 8099 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)

8099 / 1 = 8099 (the remainder is 0, so 1 is a divisor of 8099)
8099 / 2 = 4049.5 (the remainder is 1, so 2 is not a divisor of 8099)
8099 / 3 = 2699.6666666667 (the remainder is 2, so 3 is not a divisor of 8099)
...
8099 / 8098 = 1.0001234872808 (the remainder is 1, so 8098 is not a divisor of 8099)
8099 / 8099 = 1 (the remainder is 0, so 8099 is a divisor of 8099)

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 8099 (i.e. 89.994444272966). 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 $\frac{N}{d} = D$ )

8099 / 1 = 8099 (the remainder is 0, so 1 and 8099 are divisors of 8099)
8099 / 2 = 4049.5 (the remainder is 1, so 2 is not a divisor of 8099)
8099 / 3 = 2699.6666666667 (the remainder is 2, so 3 is not a divisor of 8099)
...
8099 / 88 = 92.034090909091 (the remainder is 3, so 88 is not a divisor of 8099)
8099 / 89 = 91 (the remainder is 0, so 89 and 91 are divisors of 8099)