It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 797, the answer is: yes, 797 is a prime number because it has only two distinct divisors: 1 and itself (797).
As a consequence, 797 is only a multiple of 1 and 797..
Since 797 is a prime number, 797 is also a deficient number, that is to say 797 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 797 without 797 itself (that is 1, by definition!).
Parity of 797
797 is an odd number, because it is not evenly divisible by 2.
Is 797 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 797 is about 28.231.
Thus, the square root of 797 is not an integer, and therefore 797 is not a square number.
Anyway, 797 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 797?
The square of a number (here 797) is the result of the product of this number (797) by itself (i.e., 797 × 797); the square of 797 is sometimes called "raising 797 to the power 2", or "797 squared".
As a consequence, 797 is the square root of 635 209.
Number of digits of 797
797 is a number with 3 digits.
What are the multiples of 797?
The multiples of 797 are all integers evenly divisible by 797, that is all numbers such that the remainder of the division by 797 is zero. There are infinitely many multiples of 797. The smallest multiples of 797 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 797 too, since 0 × 797 = 0
- 797: indeed, 797 is a multiple of itself, since 797 is evenly divisible by 797 (we have 797 / 797 = 1, so the remainder of this division is indeed zero)
- 1 594: indeed, 1 594 = 797 × 2
- 2 391: indeed, 2 391 = 797 × 3
- 3 188: indeed, 3 188 = 797 × 4
- 3 985: indeed, 3 985 = 797 × 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 797). 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 28.231). 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.