It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 506 138 is not a prime number.
For example, 506 138 can be divided by 2: 506 138 / 2 = 253 069.
For 506 138 to be a prime number, it would have been required that 506 138 has only two divisors, i.e., itself and 1.
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506 138 is an even number, because it is evenly divisible by 2: 506 138 / 2 = 253 069.
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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 506 138 is about 711.434.
Thus, the square root of 506 138 is not an integer, and therefore 506 138 is not a square number.
The square of a number (here 506 138) is the result of the product of this number (506 138) by itself (i.e., 506 138 × 506 138); the square of 506 138 is sometimes called "raising 506 138 to the power 2", or "506 138 squared".
The square of 506 138 is 256 175 675 044 because 506 138 × 506 138 = 506 1382 = 256 175 675 044.
As a consequence, 506 138 is the square root of 256 175 675 044.
The multiples of 506 138 are all integers evenly divisible by 506 138, that is all numbers such that the remainder of the division by 506 138 is zero. There are infinitely many multiples of 506 138. The smallest multiples of 506 138 are: