What are the divisors of 531?

1, 3, 9, 59, 177, 531

There is a total of 6 positive divisors.
The sum of these divisors is 780.
The arithmetic mean is 130.

6 odd divisors

1, 3, 9, 59, 177, 531

How to compute the divisors of 531?

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 531 by each of the numbers from 1 to 531 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)

531 / 1 = 531 (the remainder is 0, so 1 is a divisor of 531)
531 / 2 = 265.5 (the remainder is 1, so 2 is not a divisor of 531)
531 / 3 = 177 (the remainder is 0, so 3 is a divisor of 531)
...
531 / 530 = 1.0018867924528 (the remainder is 1, so 530 is not a divisor of 531)
531 / 531 = 1 (the remainder is 0, so 531 is a divisor of 531)

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 531 (i.e. 23.043437243606). 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 $\frac{N}{d} = D$ )

531 / 1 = 531 (the remainder is 0, so 1 and 531 are divisors of 531)
531 / 2 = 265.5 (the remainder is 1, so 2 is not a divisor of 531)
531 / 3 = 177 (the remainder is 0, so 3 and 177 are divisors of 531)
...
531 / 22 = 24.136363636364 (the remainder is 3, so 22 is not a divisor of 531)
531 / 23 = 23.086956521739 (the remainder is 2, so 23 is not a divisor of 531)