What are the divisors of 8173?

1, 11, 743, 8173

There is a total of 4 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 2232.

4 odd divisors

1, 11, 743, 8173

How to compute the divisors of 8173?

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 8173 by each of the numbers from 1 to 8173 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)

8173 / 1 = 8173 (the remainder is 0, so 1 is a divisor of 8173)
8173 / 2 = 4086.5 (the remainder is 1, so 2 is not a divisor of 8173)
8173 / 3 = 2724.3333333333 (the remainder is 1, so 3 is not a divisor of 8173)
...
8173 / 8172 = 1.0001223690651 (the remainder is 1, so 8172 is not a divisor of 8173)
8173 / 8173 = 1 (the remainder is 0, so 8173 is a divisor of 8173)

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 8173 (i.e. 90.404645898317). 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 $\frac{N}{d} = D$ )

8173 / 1 = 8173 (the remainder is 0, so 1 and 8173 are divisors of 8173)
8173 / 2 = 4086.5 (the remainder is 1, so 2 is not a divisor of 8173)
8173 / 3 = 2724.3333333333 (the remainder is 1, so 3 is not a divisor of 8173)
...
8173 / 89 = 91.831460674157 (the remainder is 74, so 89 is not a divisor of 8173)
8173 / 90 = 90.811111111111 (the remainder is 73, so 90 is not a divisor of 8173)