What are the divisors of 1530?

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530

There is a total of 24 positive divisors.
The sum of these divisors is 4212.
The arithmetic mean is 175.5.

12 even divisors

2, 6, 10, 18, 30, 34, 90, 102, 170, 306, 510, 1530

12 odd divisors

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

How to compute the divisors of 1530?

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 1530 by each of the numbers from 1 to 1530 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)

1530 / 1 = 1530 (the remainder is 0, so 1 is a divisor of 1530)
1530 / 2 = 765 (the remainder is 0, so 2 is a divisor of 1530)
1530 / 3 = 510 (the remainder is 0, so 3 is a divisor of 1530)
...
1530 / 1529 = 1.0006540222368 (the remainder is 1, so 1529 is not a divisor of 1530)
1530 / 1530 = 1 (the remainder is 0, so 1530 is a divisor of 1530)

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 1530 (i.e. 39.115214431216). 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 $\frac{N}{d} = D$ )

1530 / 1 = 1530 (the remainder is 0, so 1 and 1530 are divisors of 1530)
1530 / 2 = 765 (the remainder is 0, so 2 and 765 are divisors of 1530)
1530 / 3 = 510 (the remainder is 0, so 3 and 510 are divisors of 1530)
...
1530 / 38 = 40.263157894737 (the remainder is 10, so 38 is not a divisor of 1530)
1530 / 39 = 39.230769230769 (the remainder is 9, so 39 is not a divisor of 1530)