What are the divisors of 563?

1, 563

There is a total of 2 positive divisors.
The sum of these divisors is 564.
The arithmetic mean is 282.

2 odd divisors

1, 563

How to compute the divisors of 563?

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 563 by each of the numbers from 1 to 563 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)

563 / 1 = 563 (the remainder is 0, so 1 is a divisor of 563)
563 / 2 = 281.5 (the remainder is 1, so 2 is not a divisor of 563)
563 / 3 = 187.66666666667 (the remainder is 2, so 3 is not a divisor of 563)
...
563 / 562 = 1.0017793594306 (the remainder is 1, so 562 is not a divisor of 563)
563 / 563 = 1 (the remainder is 0, so 563 is a divisor of 563)

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 563 (i.e. 23.727621035409). 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 $\frac{N}{d} = D$ )

563 / 1 = 563 (the remainder is 0, so 1 and 563 are divisors of 563)
563 / 2 = 281.5 (the remainder is 1, so 2 is not a divisor of 563)
563 / 3 = 187.66666666667 (the remainder is 2, so 3 is not a divisor of 563)
...
563 / 22 = 25.590909090909 (the remainder is 13, so 22 is not a divisor of 563)
563 / 23 = 24.478260869565 (the remainder is 11, so 23 is not a divisor of 563)