What are the divisors of 595?

1, 5, 7, 17, 35, 85, 119, 595

There is a total of 8 positive divisors.
The sum of these divisors is 864.
The arithmetic mean is 108.

8 odd divisors

1, 5, 7, 17, 35, 85, 119, 595

How to compute the divisors of 595?

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 595 by each of the numbers from 1 to 595 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)

595 / 1 = 595 (the remainder is 0, so 1 is a divisor of 595)
595 / 2 = 297.5 (the remainder is 1, so 2 is not a divisor of 595)
595 / 3 = 198.33333333333 (the remainder is 1, so 3 is not a divisor of 595)
...
595 / 594 = 1.0016835016835 (the remainder is 1, so 594 is not a divisor of 595)
595 / 595 = 1 (the remainder is 0, so 595 is a divisor of 595)

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 595 (i.e. 24.392621835301). 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 $\frac{N}{d} = D$ )

595 / 1 = 595 (the remainder is 0, so 1 and 595 are divisors of 595)
595 / 2 = 297.5 (the remainder is 1, so 2 is not a divisor of 595)
595 / 3 = 198.33333333333 (the remainder is 1, so 3 is not a divisor of 595)
...
595 / 23 = 25.869565217391 (the remainder is 20, so 23 is not a divisor of 595)
595 / 24 = 24.791666666667 (the remainder is 19, so 24 is not a divisor of 595)