What are the divisors of 4594?

1, 2, 2297, 4594

There is a total of 4 positive divisors.
The sum of these divisors is 6894.
The arithmetic mean is 1723.5.

2 even divisors

2, 4594

2 odd divisors

1, 2297

How to compute the divisors of 4594?

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 4594 by each of the numbers from 1 to 4594 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)

4594 / 1 = 4594 (the remainder is 0, so 1 is a divisor of 4594)
4594 / 2 = 2297 (the remainder is 0, so 2 is a divisor of 4594)
4594 / 3 = 1531.3333333333 (the remainder is 1, so 3 is not a divisor of 4594)
...
4594 / 4593 = 1.0002177226214 (the remainder is 1, so 4593 is not a divisor of 4594)
4594 / 4594 = 1 (the remainder is 0, so 4594 is a divisor of 4594)

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 4594 (i.e. 67.779052811322). 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 $\frac{N}{d} = D$ )

4594 / 1 = 4594 (the remainder is 0, so 1 and 4594 are divisors of 4594)
4594 / 2 = 2297 (the remainder is 0, so 2 and 2297 are divisors of 4594)
4594 / 3 = 1531.3333333333 (the remainder is 1, so 3 is not a divisor of 4594)
...
4594 / 66 = 69.606060606061 (the remainder is 40, so 66 is not a divisor of 4594)
4594 / 67 = 68.567164179104 (the remainder is 38, so 67 is not a divisor of 4594)