It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 809, the answer is: yes, 809 is a prime number because it has only two distinct divisors: 1 and itself (809).
As a consequence, 809 is only a multiple of 1 and 809..
Since 809 is a prime number, 809 is also a deficient number, that is to say 809 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 809 without 809 itself (that is 1, by definition!).
Parity of 809
809 is an odd number, because it is not evenly divisible by 2.
Is 809 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 809 is about 28.443.
Thus, the square root of 809 is not an integer, and therefore 809 is not a square number.
Anyway, 809 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 809?
The square of a number (here 809) is the result of the product of this number (809) by itself (i.e., 809 × 809); the square of 809 is sometimes called "raising 809 to the power 2", or "809 squared".
As a consequence, 809 is the square root of 654 481.
Number of digits of 809
809 is a number with 3 digits.
What are the multiples of 809?
The multiples of 809 are all integers evenly divisible by 809, that is all numbers such that the remainder of the division by 809 is zero. There are infinitely many multiples of 809. The smallest multiples of 809 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 809 too, since 0 × 809 = 0
- 809: indeed, 809 is a multiple of itself, since 809 is evenly divisible by 809 (we have 809 / 809 = 1, so the remainder of this division is indeed zero)
- 1 618: indeed, 1 618 = 809 × 2
- 2 427: indeed, 2 427 = 809 × 3
- 3 236: indeed, 3 236 = 809 × 4
- 4 045: indeed, 4 045 = 809 × 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 809). 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 28.443). 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.