It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 839, the answer is: yes, 839 is a prime number because it has only two distinct divisors: 1 and itself (839).
As a consequence, 839 is only a multiple of 1 and 839..
Since 839 is a prime number, 839 is also a deficient number, that is to say 839 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 839 without 839 itself (that is 1, by definition!).
Parity of 839
839 is an odd number, because it is not evenly divisible by 2.
Is 839 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 839 is about 28.965.
Thus, the square root of 839 is not an integer, and therefore 839 is not a square number.
Anyway, 839 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 839?
The square of a number (here 839) is the result of the product of this number (839) by itself (i.e., 839 × 839); the square of 839 is sometimes called "raising 839 to the power 2", or "839 squared".
As a consequence, 839 is the square root of 703 921.
Number of digits of 839
839 is a number with 3 digits.
What are the multiples of 839?
The multiples of 839 are all integers evenly divisible by 839, that is all numbers such that the remainder of the division by 839 is zero. There are infinitely many multiples of 839. The smallest multiples of 839 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 839 too, since 0 × 839 = 0
- 839: indeed, 839 is a multiple of itself, since 839 is evenly divisible by 839 (we have 839 / 839 = 1, so the remainder of this division is indeed zero)
- 1 678: indeed, 1 678 = 839 × 2
- 2 517: indeed, 2 517 = 839 × 3
- 3 356: indeed, 3 356 = 839 × 4
- 4 195: indeed, 4 195 = 839 × 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 839). 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 28.965). 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.