What are the divisors of 9168?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 191, 382, 573, 764, 1146, 1528, 2292, 3056, 4584, 9168

There is a total of 20 positive divisors.
The sum of these divisors is 23808.
The arithmetic mean is 1190.4.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 382, 764, 1146, 1528, 2292, 3056, 4584, 9168

4 odd divisors

1, 3, 191, 573

How to compute the divisors of 9168?

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 9168 by each of the numbers from 1 to 9168 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)

9168 / 1 = 9168 (the remainder is 0, so 1 is a divisor of 9168)
9168 / 2 = 4584 (the remainder is 0, so 2 is a divisor of 9168)
9168 / 3 = 3056 (the remainder is 0, so 3 is a divisor of 9168)
...
9168 / 9167 = 1.0001090869423 (the remainder is 1, so 9167 is not a divisor of 9168)
9168 / 9168 = 1 (the remainder is 0, so 9168 is a divisor of 9168)

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 9168 (i.e. 95.749673628687). 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 $\frac{N}{d} = D$ )

9168 / 1 = 9168 (the remainder is 0, so 1 and 9168 are divisors of 9168)
9168 / 2 = 4584 (the remainder is 0, so 2 and 4584 are divisors of 9168)
9168 / 3 = 3056 (the remainder is 0, so 3 and 3056 are divisors of 9168)
...
9168 / 94 = 97.531914893617 (the remainder is 50, so 94 is not a divisor of 9168)
9168 / 95 = 96.505263157895 (the remainder is 48, so 95 is not a divisor of 9168)