What are the divisors of 9628?

1, 2, 4, 29, 58, 83, 116, 166, 332, 2407, 4814, 9628

There is a total of 12 positive divisors.
The sum of these divisors is 17640.
The arithmetic mean is 1470.

8 even divisors

2, 4, 58, 116, 166, 332, 4814, 9628

4 odd divisors

1, 29, 83, 2407

How to compute the divisors of 9628?

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 9628 by each of the numbers from 1 to 9628 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)

9628 / 1 = 9628 (the remainder is 0, so 1 is a divisor of 9628)
9628 / 2 = 4814 (the remainder is 0, so 2 is a divisor of 9628)
9628 / 3 = 3209.3333333333 (the remainder is 1, so 3 is not a divisor of 9628)
...
9628 / 9627 = 1.0001038745196 (the remainder is 1, so 9627 is not a divisor of 9628)
9628 / 9628 = 1 (the remainder is 0, so 9628 is a divisor of 9628)

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 9628 (i.e. 98.122372576289). 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 $\frac{N}{d} = D$ )

9628 / 1 = 9628 (the remainder is 0, so 1 and 9628 are divisors of 9628)
9628 / 2 = 4814 (the remainder is 0, so 2 and 4814 are divisors of 9628)
9628 / 3 = 3209.3333333333 (the remainder is 1, so 3 is not a divisor of 9628)
...
9628 / 97 = 99.257731958763 (the remainder is 25, so 97 is not a divisor of 9628)
9628 / 98 = 98.244897959184 (the remainder is 24, so 98 is not a divisor of 9628)