What are the divisors of 8299?

1, 43, 193, 8299

There is a total of 4 positive divisors.
The sum of these divisors is 8536.
The arithmetic mean is 2134.

4 odd divisors

1, 43, 193, 8299

How to compute the divisors of 8299?

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 8299 by each of the numbers from 1 to 8299 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)

8299 / 1 = 8299 (the remainder is 0, so 1 is a divisor of 8299)
8299 / 2 = 4149.5 (the remainder is 1, so 2 is not a divisor of 8299)
8299 / 3 = 2766.3333333333 (the remainder is 1, so 3 is not a divisor of 8299)
...
8299 / 8298 = 1.0001205109665 (the remainder is 1, so 8298 is not a divisor of 8299)
8299 / 8299 = 1 (the remainder is 0, so 8299 is a divisor of 8299)

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 8299 (i.e. 91.098847413126). 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 $\frac{N}{d} = D$ )

8299 / 1 = 8299 (the remainder is 0, so 1 and 8299 are divisors of 8299)
8299 / 2 = 4149.5 (the remainder is 1, so 2 is not a divisor of 8299)
8299 / 3 = 2766.3333333333 (the remainder is 1, so 3 is not a divisor of 8299)
...
8299 / 90 = 92.211111111111 (the remainder is 19, so 90 is not a divisor of 8299)
8299 / 91 = 91.197802197802 (the remainder is 18, so 91 is not a divisor of 8299)