It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 199, the answer is: yes, 199 is a prime number because it has only two distinct divisors: 1 and itself (199).
As a consequence, 199 is only a multiple of 1 and 199..
Since 199 is a prime number, 199 is also a deficient number, that is to say 199 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 199 without 199 itself (that is 1, by definition!).
Parity of 199
199 is an odd number, because it is not evenly divisible by 2.
Is 199 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 199 is about 14.107.
Thus, the square root of 199 is not an integer, and therefore 199 is not a square number.
Anyway, 199 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 199?
The square of a number (here 199) is the result of the product of this number (199) by itself (i.e., 199 × 199); the square of 199 is sometimes called "raising 199 to the power 2", or "199 squared".
As a consequence, 199 is the square root of 39 601.
Number of digits of 199
199 is a number with 3 digits.
What are the multiples of 199?
The multiples of 199 are all integers evenly divisible by 199, that is all numbers such that the remainder of the division by 199 is zero. There are infinitely many multiples of 199. The smallest multiples of 199 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 199 too, since 0 × 199 = 0
- 199: indeed, 199 is a multiple of itself, since 199 is evenly divisible by 199 (we have 199 / 199 = 1, so the remainder of this division is indeed zero)
- 398: indeed, 398 = 199 × 2
- 597: indeed, 597 = 199 × 3
- 796: indeed, 796 = 199 × 4
- 995: indeed, 995 = 199 × 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 199). 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 14.107). 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.