What are the divisors of 9048?

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 29, 39, 52, 58, 78, 87, 104, 116, 156, 174, 232, 312, 348, 377, 696, 754, 1131, 1508, 2262, 3016, 4524, 9048

There is a total of 32 positive divisors.
The sum of these divisors is 25200.
The arithmetic mean is 787.5.

24 even divisors

2, 4, 6, 8, 12, 24, 26, 52, 58, 78, 104, 116, 156, 174, 232, 312, 348, 696, 754, 1508, 2262, 3016, 4524, 9048

8 odd divisors

1, 3, 13, 29, 39, 87, 377, 1131

How to compute the divisors of 9048?

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 9048 by each of the numbers from 1 to 9048 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)

9048 / 1 = 9048 (the remainder is 0, so 1 is a divisor of 9048)
9048 / 2 = 4524 (the remainder is 0, so 2 is a divisor of 9048)
9048 / 3 = 3016 (the remainder is 0, so 3 is a divisor of 9048)
...
9048 / 9047 = 1.0001105338786 (the remainder is 1, so 9047 is not a divisor of 9048)
9048 / 9048 = 1 (the remainder is 0, so 9048 is a divisor of 9048)

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 9048 (i.e. 95.120975604753). 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 $\frac{N}{d} = D$ )

9048 / 1 = 9048 (the remainder is 0, so 1 and 9048 are divisors of 9048)
9048 / 2 = 4524 (the remainder is 0, so 2 and 4524 are divisors of 9048)
9048 / 3 = 3016 (the remainder is 0, so 3 and 3016 are divisors of 9048)
...
9048 / 94 = 96.255319148936 (the remainder is 24, so 94 is not a divisor of 9048)
9048 / 95 = 95.242105263158 (the remainder is 23, so 95 is not a divisor of 9048)