What are the divisors of 9193?

1, 29, 317, 9193

There is a total of 4 positive divisors.
The sum of these divisors is 9540.
The arithmetic mean is 2385.

4 odd divisors

1, 29, 317, 9193

How to compute the divisors of 9193?

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 9193 by each of the numbers from 1 to 9193 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)

9193 / 1 = 9193 (the remainder is 0, so 1 is a divisor of 9193)
9193 / 2 = 4596.5 (the remainder is 1, so 2 is not a divisor of 9193)
9193 / 3 = 3064.3333333333 (the remainder is 1, so 3 is not a divisor of 9193)
...
9193 / 9192 = 1.0001087902524 (the remainder is 1, so 9192 is not a divisor of 9193)
9193 / 9193 = 1 (the remainder is 0, so 9193 is a divisor of 9193)

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 9193 (i.e. 95.880133500116). 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 $\frac{N}{d} = D$ )

9193 / 1 = 9193 (the remainder is 0, so 1 and 9193 are divisors of 9193)
9193 / 2 = 4596.5 (the remainder is 1, so 2 is not a divisor of 9193)
9193 / 3 = 3064.3333333333 (the remainder is 1, so 3 is not a divisor of 9193)
...
9193 / 94 = 97.797872340426 (the remainder is 75, so 94 is not a divisor of 9193)
9193 / 95 = 96.768421052632 (the remainder is 73, so 95 is not a divisor of 9193)