What are the divisors of 9592?

1, 2, 4, 8, 11, 22, 44, 88, 109, 218, 436, 872, 1199, 2398, 4796, 9592

There is a total of 16 positive divisors.
The sum of these divisors is 19800.
The arithmetic mean is 1237.5.

12 even divisors

2, 4, 8, 22, 44, 88, 218, 436, 872, 2398, 4796, 9592

4 odd divisors

1, 11, 109, 1199

How to compute the divisors of 9592?

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 9592 by each of the numbers from 1 to 9592 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)

9592 / 1 = 9592 (the remainder is 0, so 1 is a divisor of 9592)
9592 / 2 = 4796 (the remainder is 0, so 2 is a divisor of 9592)
9592 / 3 = 3197.3333333333 (the remainder is 1, so 3 is not a divisor of 9592)
...
9592 / 9591 = 1.0001042644146 (the remainder is 1, so 9591 is not a divisor of 9592)
9592 / 9592 = 1 (the remainder is 0, so 9592 is a divisor of 9592)

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 9592 (i.e. 97.938756373562). 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 $\frac{N}{d} = D$ )

9592 / 1 = 9592 (the remainder is 0, so 1 and 9592 are divisors of 9592)
9592 / 2 = 4796 (the remainder is 0, so 2 and 4796 are divisors of 9592)
9592 / 3 = 3197.3333333333 (the remainder is 1, so 3 is not a divisor of 9592)
...
9592 / 96 = 99.916666666667 (the remainder is 88, so 96 is not a divisor of 9592)
9592 / 97 = 98.886597938144 (the remainder is 86, so 97 is not a divisor of 9592)