What are the divisors of 9648?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134, 144, 201, 268, 402, 536, 603, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648

There is a total of 30 positive divisors.
The sum of these divisors is 27404.
The arithmetic mean is 913.46666666667.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 134, 144, 268, 402, 536, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648

6 odd divisors

1, 3, 9, 67, 201, 603

How to compute the divisors of 9648?

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 9648 by each of the numbers from 1 to 9648 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)

9648 / 1 = 9648 (the remainder is 0, so 1 is a divisor of 9648)
9648 / 2 = 4824 (the remainder is 0, so 2 is a divisor of 9648)
9648 / 3 = 3216 (the remainder is 0, so 3 is a divisor of 9648)
...
9648 / 9647 = 1.0001036591687 (the remainder is 1, so 9647 is not a divisor of 9648)
9648 / 9648 = 1 (the remainder is 0, so 9648 is a divisor of 9648)

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 9648 (i.e. 98.224233262469). 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 $\frac{N}{d} = D$ )

9648 / 1 = 9648 (the remainder is 0, so 1 and 9648 are divisors of 9648)
9648 / 2 = 4824 (the remainder is 0, so 2 and 4824 are divisors of 9648)
9648 / 3 = 3216 (the remainder is 0, so 3 and 3216 are divisors of 9648)
...
9648 / 97 = 99.463917525773 (the remainder is 45, so 97 is not a divisor of 9648)
9648 / 98 = 98.448979591837 (the remainder is 44, so 98 is not a divisor of 9648)