What are the divisors of 9590?

1, 2, 5, 7, 10, 14, 35, 70, 137, 274, 685, 959, 1370, 1918, 4795, 9590

There is a total of 16 positive divisors.
The sum of these divisors is 19872.
The arithmetic mean is 1242.

8 even divisors

2, 10, 14, 70, 274, 1370, 1918, 9590

8 odd divisors

1, 5, 7, 35, 137, 685, 959, 4795

How to compute the divisors of 9590?

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 9590 by each of the numbers from 1 to 9590 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)

9590 / 1 = 9590 (the remainder is 0, so 1 is a divisor of 9590)
9590 / 2 = 4795 (the remainder is 0, so 2 is a divisor of 9590)
9590 / 3 = 3196.6666666667 (the remainder is 2, so 3 is not a divisor of 9590)
...
9590 / 9589 = 1.0001042861612 (the remainder is 1, so 9589 is not a divisor of 9590)
9590 / 9590 = 1 (the remainder is 0, so 9590 is a divisor of 9590)

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 9590 (i.e. 97.928545378761). 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 $\frac{N}{d} = D$ )

9590 / 1 = 9590 (the remainder is 0, so 1 and 9590 are divisors of 9590)
9590 / 2 = 4795 (the remainder is 0, so 2 and 4795 are divisors of 9590)
9590 / 3 = 3196.6666666667 (the remainder is 2, so 3 is not a divisor of 9590)
...
9590 / 96 = 99.895833333333 (the remainder is 86, so 96 is not a divisor of 9590)
9590 / 97 = 98.865979381443 (the remainder is 84, so 97 is not a divisor of 9590)