What are the divisors of 9024?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 47, 48, 64, 94, 96, 141, 188, 192, 282, 376, 564, 752, 1128, 1504, 2256, 3008, 4512, 9024

There is a total of 28 positive divisors.
The sum of these divisors is 24384.
The arithmetic mean is 870.85714285714.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 94, 96, 188, 192, 282, 376, 564, 752, 1128, 1504, 2256, 3008, 4512, 9024

4 odd divisors

1, 3, 47, 141

How to compute the divisors of 9024?

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 9024 by each of the numbers from 1 to 9024 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)

9024 / 1 = 9024 (the remainder is 0, so 1 is a divisor of 9024)
9024 / 2 = 4512 (the remainder is 0, so 2 is a divisor of 9024)
9024 / 3 = 3008 (the remainder is 0, so 3 is a divisor of 9024)
...
9024 / 9023 = 1.0001108278843 (the remainder is 1, so 9023 is not a divisor of 9024)
9024 / 9024 = 1 (the remainder is 0, so 9024 is a divisor of 9024)

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 9024 (i.e. 94.994736696303). 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 $\frac{N}{d} = D$ )

9024 / 1 = 9024 (the remainder is 0, so 1 and 9024 are divisors of 9024)
9024 / 2 = 4512 (the remainder is 0, so 2 and 4512 are divisors of 9024)
9024 / 3 = 3008 (the remainder is 0, so 3 and 3008 are divisors of 9024)
...
9024 / 93 = 97.032258064516 (the remainder is 3, so 93 is not a divisor of 9024)
9024 / 94 = 96 (the remainder is 0, so 94 and 96 are divisors of 9024)