What are the divisors of 9586?

1, 2, 4793, 9586

There is a total of 4 positive divisors.
The sum of these divisors is 14382.
The arithmetic mean is 3595.5.

2 even divisors

2, 9586

2 odd divisors

1, 4793

How to compute the divisors of 9586?

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 9586 by each of the numbers from 1 to 9586 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)

9586 / 1 = 9586 (the remainder is 0, so 1 is a divisor of 9586)
9586 / 2 = 4793 (the remainder is 0, so 2 is a divisor of 9586)
9586 / 3 = 3195.3333333333 (the remainder is 1, so 3 is not a divisor of 9586)
...
9586 / 9585 = 1.0001043296818 (the remainder is 1, so 9585 is not a divisor of 9586)
9586 / 9586 = 1 (the remainder is 0, so 9586 is a divisor of 9586)

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 9586 (i.e. 97.908120194394). 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 $\frac{N}{d} = D$ )

9586 / 1 = 9586 (the remainder is 0, so 1 and 9586 are divisors of 9586)
9586 / 2 = 4793 (the remainder is 0, so 2 and 4793 are divisors of 9586)
9586 / 3 = 3195.3333333333 (the remainder is 1, so 3 is not a divisor of 9586)
...
9586 / 96 = 99.854166666667 (the remainder is 82, so 96 is not a divisor of 9586)
9586 / 97 = 98.824742268041 (the remainder is 80, so 97 is not a divisor of 9586)