It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 211, the answer is: yes, 211 is a prime number because it has only two distinct divisors: 1 and itself (211).
As a consequence, 211 is only a multiple of 1 and 211..
Since 211 is a prime number, 211 is also a deficient number, that is to say 211 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 211 without 211 itself (that is 1, by definition!).
Parity of 211
211 is an odd number, because it is not evenly divisible by 2.
Is 211 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 211 is about 14.526.
Thus, the square root of 211 is not an integer, and therefore 211 is not a square number.
Anyway, 211 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 211?
The square of a number (here 211) is the result of the product of this number (211) by itself (i.e., 211 × 211); the square of 211 is sometimes called "raising 211 to the power 2", or "211 squared".
As a consequence, 211 is the square root of 44 521.
Number of digits of 211
211 is a number with 3 digits.
What are the multiples of 211?
The multiples of 211 are all integers evenly divisible by 211, that is all numbers such that the remainder of the division by 211 is zero. There are infinitely many multiples of 211. The smallest multiples of 211 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 211 too, since 0 × 211 = 0
- 211: indeed, 211 is a multiple of itself, since 211 is evenly divisible by 211 (we have 211 / 211 = 1, so the remainder of this division is indeed zero)
- 422: indeed, 422 = 211 × 2
- 633: indeed, 633 = 211 × 3
- 844: indeed, 844 = 211 × 4
- 1 055: indeed, 1 055 = 211 × 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 211). 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 14.526). 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.