It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 337, the answer is: yes, 337 is a prime number because it has only two distinct divisors: 1 and itself (337).
As a consequence, 337 is only a multiple of 1 and 337..
Since 337 is a prime number, 337 is also a deficient number, that is to say 337 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 337 without 337 itself (that is 1, by definition!).
Parity of 337
337 is an odd number, because it is not evenly divisible by 2.
Is 337 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 337 is about 18.358.
Thus, the square root of 337 is not an integer, and therefore 337 is not a square number.
Anyway, 337 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 337?
The square of a number (here 337) is the result of the product of this number (337) by itself (i.e., 337 × 337); the square of 337 is sometimes called "raising 337 to the power 2", or "337 squared".
As a consequence, 337 is the square root of 113 569.
Number of digits of 337
337 is a number with 3 digits.
What are the multiples of 337?
The multiples of 337 are all integers evenly divisible by 337, that is all numbers such that the remainder of the division by 337 is zero. There are infinitely many multiples of 337. The smallest multiples of 337 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 337 too, since 0 × 337 = 0
- 337: indeed, 337 is a multiple of itself, since 337 is evenly divisible by 337 (we have 337 / 337 = 1, so the remainder of this division is indeed zero)
- 674: indeed, 674 = 337 × 2
- 1 011: indeed, 1 011 = 337 × 3
- 1 348: indeed, 1 348 = 337 × 4
- 1 685: indeed, 1 685 = 337 × 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 337). 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 18.358). 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.