What are the divisors of 9636?

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 73, 132, 146, 219, 292, 438, 803, 876, 1606, 2409, 3212, 4818, 9636

There is a total of 24 positive divisors.
The sum of these divisors is 24864.
The arithmetic mean is 1036.

16 even divisors

2, 4, 6, 12, 22, 44, 66, 132, 146, 292, 438, 876, 1606, 3212, 4818, 9636

8 odd divisors

1, 3, 11, 33, 73, 219, 803, 2409

How to compute the divisors of 9636?

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 9636 by each of the numbers from 1 to 9636 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)

9636 / 1 = 9636 (the remainder is 0, so 1 is a divisor of 9636)
9636 / 2 = 4818 (the remainder is 0, so 2 is a divisor of 9636)
9636 / 3 = 3212 (the remainder is 0, so 3 is a divisor of 9636)
...
9636 / 9635 = 1.0001037882719 (the remainder is 1, so 9635 is not a divisor of 9636)
9636 / 9636 = 1 (the remainder is 0, so 9636 is a divisor of 9636)

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 9636 (i.e. 98.163129534464). 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 $\frac{N}{d} = D$ )

9636 / 1 = 9636 (the remainder is 0, so 1 and 9636 are divisors of 9636)
9636 / 2 = 4818 (the remainder is 0, so 2 and 4818 are divisors of 9636)
9636 / 3 = 3212 (the remainder is 0, so 3 and 3212 are divisors of 9636)
...
9636 / 97 = 99.340206185567 (the remainder is 33, so 97 is not a divisor of 9636)
9636 / 98 = 98.326530612245 (the remainder is 32, so 98 is not a divisor of 9636)