It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 191, the answer is: yes, 191 is a prime number because it has only two distinct divisors: 1 and itself (191).
As a consequence, 191 is only a multiple of 1 and 191..
Since 191 is a prime number, 191 is also a deficient number, that is to say 191 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 191 without 191 itself (that is 1, by definition!).
Parity of 191
191 is an odd number, because it is not evenly divisible by 2.
Is 191 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 191 is about 13.820.
Thus, the square root of 191 is not an integer, and therefore 191 is not a square number.
Anyway, 191 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 191?
The square of a number (here 191) is the result of the product of this number (191) by itself (i.e., 191 × 191); the square of 191 is sometimes called "raising 191 to the power 2", or "191 squared".
As a consequence, 191 is the square root of 36 481.
Number of digits of 191
191 is a number with 3 digits.
What are the multiples of 191?
The multiples of 191 are all integers evenly divisible by 191, that is all numbers such that the remainder of the division by 191 is zero. There are infinitely many multiples of 191. The smallest multiples of 191 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 191 too, since 0 × 191 = 0
- 191: indeed, 191 is a multiple of itself, since 191 is evenly divisible by 191 (we have 191 / 191 = 1, so the remainder of this division is indeed zero)
- 382: indeed, 382 = 191 × 2
- 573: indeed, 573 = 191 × 3
- 764: indeed, 764 = 191 × 4
- 955: indeed, 955 = 191 × 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 191). 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 13.820). 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.