What are the divisors of 4558?

1, 2, 43, 53, 86, 106, 2279, 4558

There is a total of 8 positive divisors.
The sum of these divisors is 7128.
The arithmetic mean is 891.

4 even divisors

2, 86, 106, 4558

4 odd divisors

1, 43, 53, 2279

How to compute the divisors of 4558?

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 4558 by each of the numbers from 1 to 4558 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)

4558 / 1 = 4558 (the remainder is 0, so 1 is a divisor of 4558)
4558 / 2 = 2279 (the remainder is 0, so 2 is a divisor of 4558)
4558 / 3 = 1519.3333333333 (the remainder is 1, so 3 is not a divisor of 4558)
...
4558 / 4557 = 1.0002194426158 (the remainder is 1, so 4557 is not a divisor of 4558)
4558 / 4558 = 1 (the remainder is 0, so 4558 is a divisor of 4558)

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 4558 (i.e. 67.512961718473). 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 $\frac{N}{d} = D$ )

4558 / 1 = 4558 (the remainder is 0, so 1 and 4558 are divisors of 4558)
4558 / 2 = 2279 (the remainder is 0, so 2 and 2279 are divisors of 4558)
4558 / 3 = 1519.3333333333 (the remainder is 1, so 3 is not a divisor of 4558)
...
4558 / 66 = 69.060606060606 (the remainder is 4, so 66 is not a divisor of 4558)
4558 / 67 = 68.029850746269 (the remainder is 2, so 67 is not a divisor of 4558)