It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 311, the answer is: yes, 311 is a prime number because it has only two distinct divisors: 1 and itself (311).
As a consequence, 311 is only a multiple of 1 and 311..
Since 311 is a prime number, 311 is also a deficient number, that is to say 311 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 311 without 311 itself (that is 1, by definition!).
Parity of 311
311 is an odd number, because it is not evenly divisible by 2.
Is 311 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 311 is about 17.635.
Thus, the square root of 311 is not an integer, and therefore 311 is not a square number.
Anyway, 311 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 311?
The square of a number (here 311) is the result of the product of this number (311) by itself (i.e., 311 × 311); the square of 311 is sometimes called "raising 311 to the power 2", or "311 squared".
As a consequence, 311 is the square root of 96 721.
Number of digits of 311
311 is a number with 3 digits.
What are the multiples of 311?
The multiples of 311 are all integers evenly divisible by 311, that is all numbers such that the remainder of the division by 311 is zero. There are infinitely many multiples of 311. The smallest multiples of 311 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 311 too, since 0 × 311 = 0
- 311: indeed, 311 is a multiple of itself, since 311 is evenly divisible by 311 (we have 311 / 311 = 1, so the remainder of this division is indeed zero)
- 622: indeed, 622 = 311 × 2
- 933: indeed, 933 = 311 × 3
- 1 244: indeed, 1 244 = 311 × 4
- 1 555: indeed, 1 555 = 311 × 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 311). 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 17.635). 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.