What are the divisors of 9584?

1, 2, 4, 8, 16, 599, 1198, 2396, 4792, 9584

There is a total of 10 positive divisors.
The sum of these divisors is 18600.
The arithmetic mean is 1860.

8 even divisors

2, 4, 8, 16, 1198, 2396, 4792, 9584

2 odd divisors

1, 599

How to compute the divisors of 9584?

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 9584 by each of the numbers from 1 to 9584 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)

9584 / 1 = 9584 (the remainder is 0, so 1 is a divisor of 9584)
9584 / 2 = 4792 (the remainder is 0, so 2 is a divisor of 9584)
9584 / 3 = 3194.6666666667 (the remainder is 2, so 3 is not a divisor of 9584)
...
9584 / 9583 = 1.0001043514557 (the remainder is 1, so 9583 is not a divisor of 9584)
9584 / 9584 = 1 (the remainder is 0, so 9584 is a divisor of 9584)

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 9584 (i.e. 97.897906004163). 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 $\frac{N}{d} = D$ )

9584 / 1 = 9584 (the remainder is 0, so 1 and 9584 are divisors of 9584)
9584 / 2 = 4792 (the remainder is 0, so 2 and 4792 are divisors of 9584)
9584 / 3 = 3194.6666666667 (the remainder is 2, so 3 is not a divisor of 9584)
...
9584 / 96 = 99.833333333333 (the remainder is 80, so 96 is not a divisor of 9584)
9584 / 97 = 98.80412371134 (the remainder is 78, so 97 is not a divisor of 9584)