What are the divisors of 9616?

1, 2, 4, 8, 16, 601, 1202, 2404, 4808, 9616

There is a total of 10 positive divisors.
The sum of these divisors is 18662.
The arithmetic mean is 1866.2.

8 even divisors

2, 4, 8, 16, 1202, 2404, 4808, 9616

2 odd divisors

1, 601

How to compute the divisors of 9616?

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 9616 by each of the numbers from 1 to 9616 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)

9616 / 1 = 9616 (the remainder is 0, so 1 is a divisor of 9616)
9616 / 2 = 4808 (the remainder is 0, so 2 is a divisor of 9616)
9616 / 3 = 3205.3333333333 (the remainder is 1, so 3 is not a divisor of 9616)
...
9616 / 9615 = 1.0001040041602 (the remainder is 1, so 9615 is not a divisor of 9616)
9616 / 9616 = 1 (the remainder is 0, so 9616 is a divisor of 9616)

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 9616 (i.e. 98.06120537705). 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 $\frac{N}{d} = D$ )

9616 / 1 = 9616 (the remainder is 0, so 1 and 9616 are divisors of 9616)
9616 / 2 = 4808 (the remainder is 0, so 2 and 4808 are divisors of 9616)
9616 / 3 = 3205.3333333333 (the remainder is 1, so 3 is not a divisor of 9616)
...
9616 / 97 = 99.134020618557 (the remainder is 13, so 97 is not a divisor of 9616)
9616 / 98 = 98.122448979592 (the remainder is 12, so 98 is not a divisor of 9616)