What are the divisors of 9596?

1, 2, 4, 2399, 4798, 9596

There is a total of 6 positive divisors.
The sum of these divisors is 16800.
The arithmetic mean is 2800.

4 even divisors

2, 4, 4798, 9596

2 odd divisors

1, 2399

How to compute the divisors of 9596?

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 9596 by each of the numbers from 1 to 9596 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)

9596 / 1 = 9596 (the remainder is 0, so 1 is a divisor of 9596)
9596 / 2 = 4798 (the remainder is 0, so 2 is a divisor of 9596)
9596 / 3 = 3198.6666666667 (the remainder is 2, so 3 is not a divisor of 9596)
...
9596 / 9595 = 1.0001042209484 (the remainder is 1, so 9595 is not a divisor of 9596)
9596 / 9596 = 1 (the remainder is 0, so 9596 is a divisor of 9596)

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 9596 (i.e. 97.959175170068). 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 $\frac{N}{d} = D$ )

9596 / 1 = 9596 (the remainder is 0, so 1 and 9596 are divisors of 9596)
9596 / 2 = 4798 (the remainder is 0, so 2 and 4798 are divisors of 9596)
9596 / 3 = 3198.6666666667 (the remainder is 2, so 3 is not a divisor of 9596)
...
9596 / 96 = 99.958333333333 (the remainder is 92, so 96 is not a divisor of 9596)
9596 / 97 = 98.927835051546 (the remainder is 90, so 97 is not a divisor of 9596)