It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 863, the answer is: yes, 863 is a prime number because it has only two distinct divisors: 1 and itself (863).
As a consequence, 863 is only a multiple of 1 and 863..
Since 863 is a prime number, 863 is also a deficient number, that is to say 863 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 863 without 863 itself (that is 1, by definition!).
Parity of 863
863 is an odd number, because it is not evenly divisible by 2.
Is 863 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 863 is about 29.377.
Thus, the square root of 863 is not an integer, and therefore 863 is not a square number.
Anyway, 863 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 863?
The square of a number (here 863) is the result of the product of this number (863) by itself (i.e., 863 × 863); the square of 863 is sometimes called "raising 863 to the power 2", or "863 squared".
As a consequence, 863 is the square root of 744 769.
Number of digits of 863
863 is a number with 3 digits.
What are the multiples of 863?
The multiples of 863 are all integers evenly divisible by 863, that is all numbers such that the remainder of the division by 863 is zero. There are infinitely many multiples of 863. The smallest multiples of 863 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 863 too, since 0 × 863 = 0
- 863: indeed, 863 is a multiple of itself, since 863 is evenly divisible by 863 (we have 863 / 863 = 1, so the remainder of this division is indeed zero)
- 1 726: indeed, 1 726 = 863 × 2
- 2 589: indeed, 2 589 = 863 × 3
- 3 452: indeed, 3 452 = 863 × 4
- 4 315: indeed, 4 315 = 863 × 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 863). 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 29.377). 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.