What are the divisors of 9582?

1, 2, 3, 6, 1597, 3194, 4791, 9582

There is a total of 8 positive divisors.
The sum of these divisors is 19176.
The arithmetic mean is 2397.

4 even divisors

2, 6, 3194, 9582

4 odd divisors

1, 3, 1597, 4791

How to compute the divisors of 9582?

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 9582 by each of the numbers from 1 to 9582 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)

9582 / 1 = 9582 (the remainder is 0, so 1 is a divisor of 9582)
9582 / 2 = 4791 (the remainder is 0, so 2 is a divisor of 9582)
9582 / 3 = 3194 (the remainder is 0, so 3 is a divisor of 9582)
...
9582 / 9581 = 1.0001043732387 (the remainder is 1, so 9581 is not a divisor of 9582)
9582 / 9582 = 1 (the remainder is 0, so 9582 is a divisor of 9582)

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 9582 (i.e. 97.887690748122). 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 $\frac{N}{d} = D$ )

9582 / 1 = 9582 (the remainder is 0, so 1 and 9582 are divisors of 9582)
9582 / 2 = 4791 (the remainder is 0, so 2 and 4791 are divisors of 9582)
9582 / 3 = 3194 (the remainder is 0, so 3 and 3194 are divisors of 9582)
...
9582 / 96 = 99.8125 (the remainder is 78, so 96 is not a divisor of 9582)
9582 / 97 = 98.783505154639 (the remainder is 76, so 97 is not a divisor of 9582)