What are the divisors of 9609?

1, 3, 3203, 9609

There is a total of 4 positive divisors.
The sum of these divisors is 12816.
The arithmetic mean is 3204.

4 odd divisors

1, 3, 3203, 9609

How to compute the divisors of 9609?

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 9609 by each of the numbers from 1 to 9609 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)

9609 / 1 = 9609 (the remainder is 0, so 1 is a divisor of 9609)
9609 / 2 = 4804.5 (the remainder is 1, so 2 is not a divisor of 9609)
9609 / 3 = 3203 (the remainder is 0, so 3 is a divisor of 9609)
...
9609 / 9608 = 1.0001040799334 (the remainder is 1, so 9608 is not a divisor of 9609)
9609 / 9609 = 1 (the remainder is 0, so 9609 is a divisor of 9609)

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 9609 (i.e. 98.025506884688). 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 $\frac{N}{d} = D$ )

9609 / 1 = 9609 (the remainder is 0, so 1 and 9609 are divisors of 9609)
9609 / 2 = 4804.5 (the remainder is 1, so 2 is not a divisor of 9609)
9609 / 3 = 3203 (the remainder is 0, so 3 and 3203 are divisors of 9609)
...
9609 / 97 = 99.061855670103 (the remainder is 6, so 97 is not a divisor of 9609)
9609 / 98 = 98.051020408163 (the remainder is 5, so 98 is not a divisor of 9609)