What are the divisors of 4539?

1, 3, 17, 51, 89, 267, 1513, 4539

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

8 odd divisors

1, 3, 17, 51, 89, 267, 1513, 4539

How to compute the divisors of 4539?

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 4539 by each of the numbers from 1 to 4539 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)

4539 / 1 = 4539 (the remainder is 0, so 1 is a divisor of 4539)
4539 / 2 = 2269.5 (the remainder is 1, so 2 is not a divisor of 4539)
4539 / 3 = 1513 (the remainder is 0, so 3 is a divisor of 4539)
...
4539 / 4538 = 1.0002203613927 (the remainder is 1, so 4538 is not a divisor of 4539)
4539 / 4539 = 1 (the remainder is 0, so 4539 is a divisor of 4539)

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 4539 (i.e. 67.372101050806). 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 $\frac{N}{d} = D$ )

4539 / 1 = 4539 (the remainder is 0, so 1 and 4539 are divisors of 4539)
4539 / 2 = 2269.5 (the remainder is 1, so 2 is not a divisor of 4539)
4539 / 3 = 1513 (the remainder is 0, so 3 and 1513 are divisors of 4539)
...
4539 / 66 = 68.772727272727 (the remainder is 51, so 66 is not a divisor of 4539)
4539 / 67 = 67.746268656716 (the remainder is 50, so 67 is not a divisor of 4539)