What are the divisors of 8273?

1, 8273

There is a total of 2 positive divisors.
The sum of these divisors is 8274.
The arithmetic mean is 4137.

2 odd divisors

1, 8273

How to compute the divisors of 8273?

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 8273 by each of the numbers from 1 to 8273 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)

8273 / 1 = 8273 (the remainder is 0, so 1 is a divisor of 8273)
8273 / 2 = 4136.5 (the remainder is 1, so 2 is not a divisor of 8273)
8273 / 3 = 2757.6666666667 (the remainder is 2, so 3 is not a divisor of 8273)
...
8273 / 8272 = 1.0001208897485 (the remainder is 1, so 8272 is not a divisor of 8273)
8273 / 8273 = 1 (the remainder is 0, so 8273 is a divisor of 8273)

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 8273 (i.e. 90.956033334793). 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 $\frac{N}{d} = D$ )

8273 / 1 = 8273 (the remainder is 0, so 1 and 8273 are divisors of 8273)
8273 / 2 = 4136.5 (the remainder is 1, so 2 is not a divisor of 8273)
8273 / 3 = 2757.6666666667 (the remainder is 2, so 3 is not a divisor of 8273)
...
8273 / 89 = 92.955056179775 (the remainder is 85, so 89 is not a divisor of 8273)
8273 / 90 = 91.922222222222 (the remainder is 83, so 90 is not a divisor of 8273)