What are the divisors of 567?

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

There is a total of 10 positive divisors.
The sum of these divisors is 968.
The arithmetic mean is 96.8.

10 odd divisors

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

How to compute the divisors of 567?

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 567 by each of the numbers from 1 to 567 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)

567 / 1 = 567 (the remainder is 0, so 1 is a divisor of 567)
567 / 2 = 283.5 (the remainder is 1, so 2 is not a divisor of 567)
567 / 3 = 189 (the remainder is 0, so 3 is a divisor of 567)
...
567 / 566 = 1.0017667844523 (the remainder is 1, so 566 is not a divisor of 567)
567 / 567 = 1 (the remainder is 0, so 567 is a divisor of 567)

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 567 (i.e. 23.811761799581). 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 $\frac{N}{d} = D$ )

567 / 1 = 567 (the remainder is 0, so 1 and 567 are divisors of 567)
567 / 2 = 283.5 (the remainder is 1, so 2 is not a divisor of 567)
567 / 3 = 189 (the remainder is 0, so 3 and 189 are divisors of 567)
...
567 / 22 = 25.772727272727 (the remainder is 17, so 22 is not a divisor of 567)
567 / 23 = 24.652173913043 (the remainder is 15, so 23 is not a divisor of 567)