What are the divisors of 4559?

1, 47, 97, 4559

There is a total of 4 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 1176.

4 odd divisors

1, 47, 97, 4559

How to compute the divisors of 4559?

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 4559 by each of the numbers from 1 to 4559 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)

4559 / 1 = 4559 (the remainder is 0, so 1 is a divisor of 4559)
4559 / 2 = 2279.5 (the remainder is 1, so 2 is not a divisor of 4559)
4559 / 3 = 1519.6666666667 (the remainder is 2, so 3 is not a divisor of 4559)
...
4559 / 4558 = 1.0002193944713 (the remainder is 1, so 4558 is not a divisor of 4559)
4559 / 4559 = 1 (the remainder is 0, so 4559 is a divisor of 4559)

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 4559 (i.e. 67.520367297579). 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 $\frac{N}{d} = D$ )

4559 / 1 = 4559 (the remainder is 0, so 1 and 4559 are divisors of 4559)
4559 / 2 = 2279.5 (the remainder is 1, so 2 is not a divisor of 4559)
4559 / 3 = 1519.6666666667 (the remainder is 2, so 3 is not a divisor of 4559)
...
4559 / 66 = 69.075757575758 (the remainder is 5, so 66 is not a divisor of 4559)
4559 / 67 = 68.044776119403 (the remainder is 3, so 67 is not a divisor of 4559)