What are the divisors of 9595?

1, 5, 19, 95, 101, 505, 1919, 9595

There is a total of 8 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 1530.

8 odd divisors

1, 5, 19, 95, 101, 505, 1919, 9595

How to compute the divisors of 9595?

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 9595 by each of the numbers from 1 to 9595 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)

9595 / 1 = 9595 (the remainder is 0, so 1 is a divisor of 9595)
9595 / 2 = 4797.5 (the remainder is 1, so 2 is not a divisor of 9595)
9595 / 3 = 3198.3333333333 (the remainder is 1, so 3 is not a divisor of 9595)
...
9595 / 9594 = 1.0001042318115 (the remainder is 1, so 9594 is not a divisor of 9595)
9595 / 9595 = 1 (the remainder is 0, so 9595 is a divisor of 9595)

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 9595 (i.e. 97.954070869975). 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 $\frac{N}{d} = D$ )

9595 / 1 = 9595 (the remainder is 0, so 1 and 9595 are divisors of 9595)
9595 / 2 = 4797.5 (the remainder is 1, so 2 is not a divisor of 9595)
9595 / 3 = 3198.3333333333 (the remainder is 1, so 3 is not a divisor of 9595)
...
9595 / 96 = 99.947916666667 (the remainder is 91, so 96 is not a divisor of 9595)
9595 / 97 = 98.917525773196 (the remainder is 89, so 97 is not a divisor of 9595)