It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 38 508 is not a prime number.
For example, 38 508 can be divided by 2: 38 508 / 2 = 19 254.
For 38 508 to be a prime number, it would have been required that 38 508 has only two divisors, i.e., itself and 1.
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38 508 is an even number, because it is evenly divisible by 2: 38 508 / 2 = 19 254.
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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 38 508 is about 196.235.
Thus, the square root of 38 508 is not an integer, and therefore 38 508 is not a square number.
The square of a number (here 38 508) is the result of the product of this number (38 508) by itself (i.e., 38 508 × 38 508); the square of 38 508 is sometimes called "raising 38 508 to the power 2", or "38 508 squared".
The square of 38 508 is 1 482 866 064 because 38 508 × 38 508 = 38 5082 = 1 482 866 064.
As a consequence, 38 508 is the square root of 1 482 866 064.
The multiples of 38 508 are all integers evenly divisible by 38 508, that is all numbers such that the remainder of the division by 38 508 is zero. There are infinitely many multiples of 38 508. The smallest multiples of 38 508 are: