What are the divisors of 4589?

1, 13, 353, 4589

There is a total of 4 positive divisors.
The sum of these divisors is 4956.
The arithmetic mean is 1239.

4 odd divisors

1, 13, 353, 4589

How to compute the divisors of 4589?

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 4589 by each of the numbers from 1 to 4589 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)

4589 / 1 = 4589 (the remainder is 0, so 1 is a divisor of 4589)
4589 / 2 = 2294.5 (the remainder is 1, so 2 is not a divisor of 4589)
4589 / 3 = 1529.6666666667 (the remainder is 2, so 3 is not a divisor of 4589)
...
4589 / 4588 = 1.0002179598954 (the remainder is 1, so 4588 is not a divisor of 4589)
4589 / 4589 = 1 (the remainder is 0, so 4589 is a divisor of 4589)

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 4589 (i.e. 67.74215821776). 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 $\frac{N}{d} = D$ )

4589 / 1 = 4589 (the remainder is 0, so 1 and 4589 are divisors of 4589)
4589 / 2 = 2294.5 (the remainder is 1, so 2 is not a divisor of 4589)
4589 / 3 = 1529.6666666667 (the remainder is 2, so 3 is not a divisor of 4589)
...
4589 / 66 = 69.530303030303 (the remainder is 35, so 66 is not a divisor of 4589)
4589 / 67 = 68.492537313433 (the remainder is 33, so 67 is not a divisor of 4589)