It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 331, the answer is: yes, 331 is a prime number because it has only two distinct divisors: 1 and itself (331).
As a consequence, 331 is only a multiple of 1 and 331..
Since 331 is a prime number, 331 is also a deficient number, that is to say 331 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 331 without 331 itself (that is 1, by definition!).
Parity of 331
331 is an odd number, because it is not evenly divisible by 2.
Is 331 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 331 is about 18.193.
Thus, the square root of 331 is not an integer, and therefore 331 is not a square number.
Anyway, 331 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 331?
The square of a number (here 331) is the result of the product of this number (331) by itself (i.e., 331 × 331); the square of 331 is sometimes called "raising 331 to the power 2", or "331 squared".
As a consequence, 331 is the square root of 109 561.
Number of digits of 331
331 is a number with 3 digits.
What are the multiples of 331?
The multiples of 331 are all integers evenly divisible by 331, that is all numbers such that the remainder of the division by 331 is zero. There are infinitely many multiples of 331. The smallest multiples of 331 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 331 too, since 0 × 331 = 0
- 331: indeed, 331 is a multiple of itself, since 331 is evenly divisible by 331 (we have 331 / 331 = 1, so the remainder of this division is indeed zero)
- 662: indeed, 662 = 331 × 2
- 993: indeed, 993 = 331 × 3
- 1 324: indeed, 1 324 = 331 × 4
- 1 655: indeed, 1 655 = 331 × 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 331). 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 18.193). 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.