It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 271, the answer is: yes, 271 is a prime number because it has only two distinct divisors: 1 and itself (271).
As a consequence, 271 is only a multiple of 1 and 271..
Since 271 is a prime number, 271 is also a deficient number, that is to say 271 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 271 without 271 itself (that is 1, by definition!).
Parity of 271
271 is an odd number, because it is not evenly divisible by 2.
Is 271 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 271 is about 16.462.
Thus, the square root of 271 is not an integer, and therefore 271 is not a square number.
Anyway, 271 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 271?
The square of a number (here 271) is the result of the product of this number (271) by itself (i.e., 271 × 271); the square of 271 is sometimes called "raising 271 to the power 2", or "271 squared".
As a consequence, 271 is the square root of 73 441.
Number of digits of 271
271 is a number with 3 digits.
What are the multiples of 271?
The multiples of 271 are all integers evenly divisible by 271, that is all numbers such that the remainder of the division by 271 is zero. There are infinitely many multiples of 271. The smallest multiples of 271 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 271 too, since 0 × 271 = 0
- 271: indeed, 271 is a multiple of itself, since 271 is evenly divisible by 271 (we have 271 / 271 = 1, so the remainder of this division is indeed zero)
- 542: indeed, 542 = 271 × 2
- 813: indeed, 813 = 271 × 3
- 1 084: indeed, 1 084 = 271 × 4
- 1 355: indeed, 1 355 = 271 × 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 271). 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 16.462). 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.