What are the divisors of 9624?

1, 2, 3, 4, 6, 8, 12, 24, 401, 802, 1203, 1604, 2406, 3208, 4812, 9624

There is a total of 16 positive divisors.
The sum of these divisors is 24120.
The arithmetic mean is 1507.5.

12 even divisors

2, 4, 6, 8, 12, 24, 802, 1604, 2406, 3208, 4812, 9624

4 odd divisors

1, 3, 401, 1203

How to compute the divisors of 9624?

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 9624 by each of the numbers from 1 to 9624 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)

9624 / 1 = 9624 (the remainder is 0, so 1 is a divisor of 9624)
9624 / 2 = 4812 (the remainder is 0, so 2 is a divisor of 9624)
9624 / 3 = 3208 (the remainder is 0, so 3 is a divisor of 9624)
...
9624 / 9623 = 1.0001039176972 (the remainder is 1, so 9623 is not a divisor of 9624)
9624 / 9624 = 1 (the remainder is 0, so 9624 is a divisor of 9624)

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 9624 (i.e. 98.101987747446). 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 $\frac{N}{d} = D$ )

9624 / 1 = 9624 (the remainder is 0, so 1 and 9624 are divisors of 9624)
9624 / 2 = 4812 (the remainder is 0, so 2 and 4812 are divisors of 9624)
9624 / 3 = 3208 (the remainder is 0, so 3 and 3208 are divisors of 9624)
...
9624 / 97 = 99.216494845361 (the remainder is 21, so 97 is not a divisor of 9624)
9624 / 98 = 98.204081632653 (the remainder is 20, so 98 is not a divisor of 9624)