What are the divisors of 9606?

1, 2, 3, 6, 1601, 3202, 4803, 9606

There is a total of 8 positive divisors.
The sum of these divisors is 19224.
The arithmetic mean is 2403.

4 even divisors

2, 6, 3202, 9606

4 odd divisors

1, 3, 1601, 4803

How to compute the divisors of 9606?

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 9606 by each of the numbers from 1 to 9606 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)

9606 / 1 = 9606 (the remainder is 0, so 1 is a divisor of 9606)
9606 / 2 = 4803 (the remainder is 0, so 2 is a divisor of 9606)
9606 / 3 = 3202 (the remainder is 0, so 3 is a divisor of 9606)
...
9606 / 9605 = 1.0001041124414 (the remainder is 1, so 9605 is not a divisor of 9606)
9606 / 9606 = 1 (the remainder is 0, so 9606 is a divisor of 9606)

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 9606 (i.e. 98.010203550447). 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 $\frac{N}{d} = D$ )

9606 / 1 = 9606 (the remainder is 0, so 1 and 9606 are divisors of 9606)
9606 / 2 = 4803 (the remainder is 0, so 2 and 4803 are divisors of 9606)
9606 / 3 = 3202 (the remainder is 0, so 3 and 3202 are divisors of 9606)
...
9606 / 97 = 99.030927835052 (the remainder is 3, so 97 is not a divisor of 9606)
9606 / 98 = 98.020408163265 (the remainder is 2, so 98 is not a divisor of 9606)