What are the divisors of 530?

1, 2, 5, 10, 53, 106, 265, 530

There is a total of 8 positive divisors.
The sum of these divisors is 972.
The arithmetic mean is 121.5.

4 even divisors

2, 10, 106, 530

4 odd divisors

1, 5, 53, 265

How to compute the divisors of 530?

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 530 by each of the numbers from 1 to 530 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)

530 / 1 = 530 (the remainder is 0, so 1 is a divisor of 530)
530 / 2 = 265 (the remainder is 0, so 2 is a divisor of 530)
530 / 3 = 176.66666666667 (the remainder is 2, so 3 is not a divisor of 530)
...
530 / 529 = 1.0018903591682 (the remainder is 1, so 529 is not a divisor of 530)
530 / 530 = 1 (the remainder is 0, so 530 is a divisor of 530)

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 530 (i.e. 23.021728866443). 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 $\frac{N}{d} = D$ )

530 / 1 = 530 (the remainder is 0, so 1 and 530 are divisors of 530)
530 / 2 = 265 (the remainder is 0, so 2 and 265 are divisors of 530)
530 / 3 = 176.66666666667 (the remainder is 2, so 3 is not a divisor of 530)
...
530 / 22 = 24.090909090909 (the remainder is 2, so 22 is not a divisor of 530)
530 / 23 = 23.04347826087 (the remainder is 1, so 23 is not a divisor of 530)