What are the divisors of 9600?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

There is a total of 48 positive divisors.
The sum of these divisors is 31620.
The arithmetic mean is 658.75.

42 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 50, 60, 64, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

6 odd divisors

1, 3, 5, 15, 25, 75

How to compute the divisors of 9600?

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 9600 by each of the numbers from 1 to 9600 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)

9600 / 1 = 9600 (the remainder is 0, so 1 is a divisor of 9600)
9600 / 2 = 4800 (the remainder is 0, so 2 is a divisor of 9600)
9600 / 3 = 3200 (the remainder is 0, so 3 is a divisor of 9600)
...
9600 / 9599 = 1.0001041775185 (the remainder is 1, so 9599 is not a divisor of 9600)
9600 / 9600 = 1 (the remainder is 0, so 9600 is a divisor of 9600)

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 9600 (i.e. 97.979589711327). 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 $\frac{N}{d} = D$ )

9600 / 1 = 9600 (the remainder is 0, so 1 and 9600 are divisors of 9600)
9600 / 2 = 4800 (the remainder is 0, so 2 and 4800 are divisors of 9600)
9600 / 3 = 3200 (the remainder is 0, so 3 and 3200 are divisors of 9600)
...
9600 / 96 = 100 (the remainder is 0, so 96 and 100 are divisors of 9600)
9600 / 97 = 98.969072164948 (the remainder is 94, so 97 is not a divisor of 9600)