What are the divisors of 9173?

1, 9173

There is a total of 2 positive divisors.
The sum of these divisors is 9174.
The arithmetic mean is 4587.

2 odd divisors

1, 9173

How to compute the divisors of 9173?

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 9173 by each of the numbers from 1 to 9173 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)

9173 / 1 = 9173 (the remainder is 0, so 1 is a divisor of 9173)
9173 / 2 = 4586.5 (the remainder is 1, so 2 is not a divisor of 9173)
9173 / 3 = 3057.6666666667 (the remainder is 2, so 3 is not a divisor of 9173)
...
9173 / 9172 = 1.0001090274749 (the remainder is 1, so 9172 is not a divisor of 9173)
9173 / 9173 = 1 (the remainder is 0, so 9173 is a divisor of 9173)

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 9173 (i.e. 95.775779819326). 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 $\frac{N}{d} = D$ )

9173 / 1 = 9173 (the remainder is 0, so 1 and 9173 are divisors of 9173)
9173 / 2 = 4586.5 (the remainder is 1, so 2 is not a divisor of 9173)
9173 / 3 = 3057.6666666667 (the remainder is 2, so 3 is not a divisor of 9173)
...
9173 / 94 = 97.585106382979 (the remainder is 55, so 94 is not a divisor of 9173)
9173 / 95 = 96.557894736842 (the remainder is 53, so 95 is not a divisor of 9173)