What are the divisors of 9072?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 252, 324, 336, 378, 432, 504, 567, 648, 756, 1008, 1134, 1296, 1512, 2268, 3024, 4536, 9072

There is a total of 50 positive divisors.
The sum of these divisors is 30008.
The arithmetic mean is 600.16.

40 even divisors

2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 36, 42, 48, 54, 56, 72, 84, 108, 112, 126, 144, 162, 168, 216, 252, 324, 336, 378, 432, 504, 648, 756, 1008, 1134, 1296, 1512, 2268, 3024, 4536, 9072

10 odd divisors

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

How to compute the divisors of 9072?

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 9072 by each of the numbers from 1 to 9072 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)

9072 / 1 = 9072 (the remainder is 0, so 1 is a divisor of 9072)
9072 / 2 = 4536 (the remainder is 0, so 2 is a divisor of 9072)
9072 / 3 = 3024 (the remainder is 0, so 3 is a divisor of 9072)
...
9072 / 9071 = 1.0001102414287 (the remainder is 1, so 9071 is not a divisor of 9072)
9072 / 9072 = 1 (the remainder is 0, so 9072 is a divisor of 9072)

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 9072 (i.e. 95.247047198325). 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 $\frac{N}{d} = D$ )

9072 / 1 = 9072 (the remainder is 0, so 1 and 9072 are divisors of 9072)
9072 / 2 = 4536 (the remainder is 0, so 2 and 4536 are divisors of 9072)
9072 / 3 = 3024 (the remainder is 0, so 3 and 3024 are divisors of 9072)
...
9072 / 94 = 96.510638297872 (the remainder is 48, so 94 is not a divisor of 9072)
9072 / 95 = 95.494736842105 (the remainder is 47, so 95 is not a divisor of 9072)