What are the divisors of 4595?

1, 5, 919, 4595

There is a total of 4 positive divisors.
The sum of these divisors is 5520.
The arithmetic mean is 1380.

4 odd divisors

1, 5, 919, 4595

How to compute the divisors of 4595?

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 4595 by each of the numbers from 1 to 4595 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)

4595 / 1 = 4595 (the remainder is 0, so 1 is a divisor of 4595)
4595 / 2 = 2297.5 (the remainder is 1, so 2 is not a divisor of 4595)
4595 / 3 = 1531.6666666667 (the remainder is 2, so 3 is not a divisor of 4595)
...
4595 / 4594 = 1.0002176752286 (the remainder is 1, so 4594 is not a divisor of 4595)
4595 / 4595 = 1 (the remainder is 0, so 4595 is a divisor of 4595)

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 4595 (i.e. 67.786429320329). 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 $\frac{N}{d} = D$ )

4595 / 1 = 4595 (the remainder is 0, so 1 and 4595 are divisors of 4595)
4595 / 2 = 2297.5 (the remainder is 1, so 2 is not a divisor of 4595)
4595 / 3 = 1531.6666666667 (the remainder is 2, so 3 is not a divisor of 4595)
...
4595 / 66 = 69.621212121212 (the remainder is 41, so 66 is not a divisor of 4595)
4595 / 67 = 68.582089552239 (the remainder is 39, so 67 is not a divisor of 4595)