What are the divisors of 4530?

1, 2, 3, 5, 6, 10, 15, 30, 151, 302, 453, 755, 906, 1510, 2265, 4530

There is a total of 16 positive divisors.
The sum of these divisors is 10944.
The arithmetic mean is 684.

8 even divisors

2, 6, 10, 30, 302, 906, 1510, 4530

8 odd divisors

1, 3, 5, 15, 151, 453, 755, 2265

How to compute the divisors of 4530?

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 4530 by each of the numbers from 1 to 4530 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)

4530 / 1 = 4530 (the remainder is 0, so 1 is a divisor of 4530)
4530 / 2 = 2265 (the remainder is 0, so 2 is a divisor of 4530)
4530 / 3 = 1510 (the remainder is 0, so 3 is a divisor of 4530)
...
4530 / 4529 = 1.0002207992934 (the remainder is 1, so 4529 is not a divisor of 4530)
4530 / 4530 = 1 (the remainder is 0, so 4530 is a divisor of 4530)

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 4530 (i.e. 67.305274681855). 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 $\frac{N}{d} = D$ )

4530 / 1 = 4530 (the remainder is 0, so 1 and 4530 are divisors of 4530)
4530 / 2 = 2265 (the remainder is 0, so 2 and 2265 are divisors of 4530)
4530 / 3 = 1510 (the remainder is 0, so 3 and 1510 are divisors of 4530)
...
4530 / 66 = 68.636363636364 (the remainder is 42, so 66 is not a divisor of 4530)
4530 / 67 = 67.611940298507 (the remainder is 41, so 67 is not a divisor of 4530)