What are the divisors of 8301?

1, 3, 2767, 8301

There is a total of 4 positive divisors.
The sum of these divisors is 11072.
The arithmetic mean is 2768.

4 odd divisors

1, 3, 2767, 8301

How to compute the divisors of 8301?

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 8301 by each of the numbers from 1 to 8301 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)

8301 / 1 = 8301 (the remainder is 0, so 1 is a divisor of 8301)
8301 / 2 = 4150.5 (the remainder is 1, so 2 is not a divisor of 8301)
8301 / 3 = 2767 (the remainder is 0, so 3 is a divisor of 8301)
...
8301 / 8300 = 1.0001204819277 (the remainder is 1, so 8300 is not a divisor of 8301)
8301 / 8301 = 1 (the remainder is 0, so 8301 is a divisor of 8301)

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 8301 (i.e. 91.109823839145). 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 $\frac{N}{d} = D$ )

8301 / 1 = 8301 (the remainder is 0, so 1 and 8301 are divisors of 8301)
8301 / 2 = 4150.5 (the remainder is 1, so 2 is not a divisor of 8301)
8301 / 3 = 2767 (the remainder is 0, so 3 and 2767 are divisors of 8301)
...
8301 / 90 = 92.233333333333 (the remainder is 21, so 90 is not a divisor of 8301)
8301 / 91 = 91.21978021978 (the remainder is 20, so 91 is not a divisor of 8301)