What are the divisors of 9192?

1, 2, 3, 4, 6, 8, 12, 24, 383, 766, 1149, 1532, 2298, 3064, 4596, 9192

There is a total of 16 positive divisors.
The sum of these divisors is 23040.
The arithmetic mean is 1440.

12 even divisors

2, 4, 6, 8, 12, 24, 766, 1532, 2298, 3064, 4596, 9192

4 odd divisors

1, 3, 383, 1149

How to compute the divisors of 9192?

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 9192 by each of the numbers from 1 to 9192 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)

9192 / 1 = 9192 (the remainder is 0, so 1 is a divisor of 9192)
9192 / 2 = 4596 (the remainder is 0, so 2 is a divisor of 9192)
9192 / 3 = 3064 (the remainder is 0, so 3 is a divisor of 9192)
...
9192 / 9191 = 1.000108802089 (the remainder is 1, so 9191 is not a divisor of 9192)
9192 / 9192 = 1 (the remainder is 0, so 9192 is a divisor of 9192)

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 9192 (i.e. 95.874918513655). 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 $\frac{N}{d} = D$ )

9192 / 1 = 9192 (the remainder is 0, so 1 and 9192 are divisors of 9192)
9192 / 2 = 4596 (the remainder is 0, so 2 and 4596 are divisors of 9192)
9192 / 3 = 3064 (the remainder is 0, so 3 and 3064 are divisors of 9192)
...
9192 / 94 = 97.787234042553 (the remainder is 74, so 94 is not a divisor of 9192)
9192 / 95 = 96.757894736842 (the remainder is 72, so 95 is not a divisor of 9192)