What are the divisors of 9183?

1, 3, 3061, 9183

There is a total of 4 positive divisors.
The sum of these divisors is 12248.
The arithmetic mean is 3062.

4 odd divisors

1, 3, 3061, 9183

How to compute the divisors of 9183?

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 9183 by each of the numbers from 1 to 9183 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)

9183 / 1 = 9183 (the remainder is 0, so 1 is a divisor of 9183)
9183 / 2 = 4591.5 (the remainder is 1, so 2 is not a divisor of 9183)
9183 / 3 = 3061 (the remainder is 0, so 3 is a divisor of 9183)
...
9183 / 9182 = 1.0001089087345 (the remainder is 1, so 9182 is not a divisor of 9183)
9183 / 9183 = 1 (the remainder is 0, so 9183 is a divisor of 9183)

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 9183 (i.e. 95.827970864461). 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 $\frac{N}{d} = D$ )

9183 / 1 = 9183 (the remainder is 0, so 1 and 9183 are divisors of 9183)
9183 / 2 = 4591.5 (the remainder is 1, so 2 is not a divisor of 9183)
9183 / 3 = 3061 (the remainder is 0, so 3 and 3061 are divisors of 9183)
...
9183 / 94 = 97.691489361702 (the remainder is 65, so 94 is not a divisor of 9183)
9183 / 95 = 96.663157894737 (the remainder is 63, so 95 is not a divisor of 9183)