What are the divisors of 9587?

1, 9587

There is a total of 2 positive divisors.
The sum of these divisors is 9588.
The arithmetic mean is 4794.

2 odd divisors

1, 9587

How to compute the divisors of 9587?

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 9587 by each of the numbers from 1 to 9587 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)

9587 / 1 = 9587 (the remainder is 0, so 1 is a divisor of 9587)
9587 / 2 = 4793.5 (the remainder is 1, so 2 is not a divisor of 9587)
9587 / 3 = 3195.6666666667 (the remainder is 2, so 3 is not a divisor of 9587)
...
9587 / 9586 = 1.0001043187982 (the remainder is 1, so 9586 is not a divisor of 9587)
9587 / 9587 = 1 (the remainder is 0, so 9587 is a divisor of 9587)

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 9587 (i.e. 97.913226889936). 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 $\frac{N}{d} = D$ )

9587 / 1 = 9587 (the remainder is 0, so 1 and 9587 are divisors of 9587)
9587 / 2 = 4793.5 (the remainder is 1, so 2 is not a divisor of 9587)
9587 / 3 = 3195.6666666667 (the remainder is 2, so 3 is not a divisor of 9587)
...
9587 / 96 = 99.864583333333 (the remainder is 83, so 96 is not a divisor of 9587)
9587 / 97 = 98.835051546392 (the remainder is 81, so 97 is not a divisor of 9587)