What are the divisors of 9589?

1, 43, 223, 9589

There is a total of 4 positive divisors.
The sum of these divisors is 9856.
The arithmetic mean is 2464.

4 odd divisors

1, 43, 223, 9589

How to compute the divisors of 9589?

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 9589 by each of the numbers from 1 to 9589 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)

9589 / 1 = 9589 (the remainder is 0, so 1 is a divisor of 9589)
9589 / 2 = 4794.5 (the remainder is 1, so 2 is not a divisor of 9589)
9589 / 3 = 3196.3333333333 (the remainder is 1, so 3 is not a divisor of 9589)
...
9589 / 9588 = 1.000104297038 (the remainder is 1, so 9588 is not a divisor of 9589)
9589 / 9589 = 1 (the remainder is 0, so 9589 is a divisor of 9589)

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 9589 (i.e. 97.923439482077). 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 $\frac{N}{d} = D$ )

9589 / 1 = 9589 (the remainder is 0, so 1 and 9589 are divisors of 9589)
9589 / 2 = 4794.5 (the remainder is 1, so 2 is not a divisor of 9589)
9589 / 3 = 3196.3333333333 (the remainder is 1, so 3 is not a divisor of 9589)
...
9589 / 96 = 99.885416666667 (the remainder is 85, so 96 is not a divisor of 9589)
9589 / 97 = 98.855670103093 (the remainder is 83, so 97 is not a divisor of 9589)