It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 563, the answer is: yes, 563 is a prime number because it has only two distinct divisors: 1 and itself (563).
As a consequence, 563 is only a multiple of 1 and 563..
Since 563 is a prime number, 563 is also a deficient number, that is to say 563 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 563 without 563 itself (that is 1, by definition!).
Parity of 563
563 is an odd number, because it is not evenly divisible by 2.
Is 563 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 563 is about 23.728.
Thus, the square root of 563 is not an integer, and therefore 563 is not a square number.
Anyway, 563 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 563?
The square of a number (here 563) is the result of the product of this number (563) by itself (i.e., 563 × 563); the square of 563 is sometimes called "raising 563 to the power 2", or "563 squared".
As a consequence, 563 is the square root of 316 969.
Number of digits of 563
563 is a number with 3 digits.
What are the multiples of 563?
The multiples of 563 are all integers evenly divisible by 563, that is all numbers such that the remainder of the division by 563 is zero. There are infinitely many multiples of 563. The smallest multiples of 563 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 563 too, since 0 × 563 = 0
- 563: indeed, 563 is a multiple of itself, since 563 is evenly divisible by 563 (we have 563 / 563 = 1, so the remainder of this division is indeed zero)
- 1 126: indeed, 1 126 = 563 × 2
- 1 689: indeed, 1 689 = 563 × 3
- 2 252: indeed, 2 252 = 563 × 4
- 2 815: indeed, 2 815 = 563 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 563). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 23.728). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.