It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 937, the answer is: yes, 937 is a prime number because it has only two distinct divisors: 1 and itself (937).
As a consequence, 937 is only a multiple of 1 and 937..
Since 937 is a prime number, 937 is also a deficient number, that is to say 937 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 937 without 937 itself (that is 1, by definition!).
Parity of 937
937 is an odd number, because it is not evenly divisible by 2.
Is 937 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 937 is about 30.610.
Thus, the square root of 937 is not an integer, and therefore 937 is not a square number.
Anyway, 937 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 937?
The square of a number (here 937) is the result of the product of this number (937) by itself (i.e., 937 × 937); the square of 937 is sometimes called "raising 937 to the power 2", or "937 squared".
As a consequence, 937 is the square root of 877 969.
Number of digits of 937
937 is a number with 3 digits.
What are the multiples of 937?
The multiples of 937 are all integers evenly divisible by 937, that is all numbers such that the remainder of the division by 937 is zero. There are infinitely many multiples of 937. The smallest multiples of 937 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 937 too, since 0 × 937 = 0
- 937: indeed, 937 is a multiple of itself, since 937 is evenly divisible by 937 (we have 937 / 937 = 1, so the remainder of this division is indeed zero)
- 1 874: indeed, 1 874 = 937 × 2
- 2 811: indeed, 2 811 = 937 × 3
- 3 748: indeed, 3 748 = 937 × 4
- 4 685: indeed, 4 685 = 937 × 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 937). 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 30.610). 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.