What are the divisors of 9630?

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 107, 214, 321, 535, 642, 963, 1070, 1605, 1926, 3210, 4815, 9630

There is a total of 24 positive divisors.
The sum of these divisors is 25272.
The arithmetic mean is 1053.

12 even divisors

2, 6, 10, 18, 30, 90, 214, 642, 1070, 1926, 3210, 9630

12 odd divisors

1, 3, 5, 9, 15, 45, 107, 321, 535, 963, 1605, 4815

How to compute the divisors of 9630?

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 9630 by each of the numbers from 1 to 9630 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)

9630 / 1 = 9630 (the remainder is 0, so 1 is a divisor of 9630)
9630 / 2 = 4815 (the remainder is 0, so 2 is a divisor of 9630)
9630 / 3 = 3210 (the remainder is 0, so 3 is a divisor of 9630)
...
9630 / 9629 = 1.0001038529442 (the remainder is 1, so 9629 is not a divisor of 9630)
9630 / 9630 = 1 (the remainder is 0, so 9630 is a divisor of 9630)

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 9630 (i.e. 98.132563402777). 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 $\frac{N}{d} = D$ )

9630 / 1 = 9630 (the remainder is 0, so 1 and 9630 are divisors of 9630)
9630 / 2 = 4815 (the remainder is 0, so 2 and 4815 are divisors of 9630)
9630 / 3 = 3210 (the remainder is 0, so 3 and 3210 are divisors of 9630)
...
9630 / 97 = 99.278350515464 (the remainder is 27, so 97 is not a divisor of 9630)
9630 / 98 = 98.265306122449 (the remainder is 26, so 98 is not a divisor of 9630)