What are the divisors of 8293?

1, 8293

There is a total of 2 positive divisors.
The sum of these divisors is 8294.
The arithmetic mean is 4147.

2 odd divisors

1, 8293

How to compute the divisors of 8293?

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 8293 by each of the numbers from 1 to 8293 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)

8293 / 1 = 8293 (the remainder is 0, so 1 is a divisor of 8293)
8293 / 2 = 4146.5 (the remainder is 1, so 2 is not a divisor of 8293)
8293 / 3 = 2764.3333333333 (the remainder is 1, so 3 is not a divisor of 8293)
...
8293 / 8292 = 1.0001205981669 (the remainder is 1, so 8292 is not a divisor of 8293)
8293 / 8293 = 1 (the remainder is 0, so 8293 is a divisor of 8293)

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 8293 (i.e. 91.065910196956). 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 $\frac{N}{d} = D$ )

8293 / 1 = 8293 (the remainder is 0, so 1 and 8293 are divisors of 8293)
8293 / 2 = 4146.5 (the remainder is 1, so 2 is not a divisor of 8293)
8293 / 3 = 2764.3333333333 (the remainder is 1, so 3 is not a divisor of 8293)
...
8293 / 90 = 92.144444444444 (the remainder is 13, so 90 is not a divisor of 8293)
8293 / 91 = 91.131868131868 (the remainder is 12, so 91 is not a divisor of 8293)