What are the divisors of 573?

1, 3, 191, 573

There is a total of 4 positive divisors.
The sum of these divisors is 768.
The arithmetic mean is 192.

4 odd divisors

1, 3, 191, 573

How to compute the divisors of 573?

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 573 by each of the numbers from 1 to 573 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)

573 / 1 = 573 (the remainder is 0, so 1 is a divisor of 573)
573 / 2 = 286.5 (the remainder is 1, so 2 is not a divisor of 573)
573 / 3 = 191 (the remainder is 0, so 3 is a divisor of 573)
...
573 / 572 = 1.0017482517483 (the remainder is 1, so 572 is not a divisor of 573)
573 / 573 = 1 (the remainder is 0, so 573 is a divisor of 573)

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 573 (i.e. 23.937418407172). 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 $\frac{N}{d} = D$ )

573 / 1 = 573 (the remainder is 0, so 1 and 573 are divisors of 573)
573 / 2 = 286.5 (the remainder is 1, so 2 is not a divisor of 573)
573 / 3 = 191 (the remainder is 0, so 3 and 191 are divisors of 573)
...
573 / 22 = 26.045454545455 (the remainder is 1, so 22 is not a divisor of 573)
573 / 23 = 24.913043478261 (the remainder is 21, so 23 is not a divisor of 573)