It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 38 972 is not a prime number.
For example, 38 972 can be divided by 2: 38 972 / 2 = 19 486.
For 38 972 to be a prime number, it would have been required that 38 972 has only two divisors, i.e., itself and 1.
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38 972 is an even number, because it is evenly divisible by 2: 38 972 / 2 = 19 486.
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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 38 972 is about 197.413.
Thus, the square root of 38 972 is not an integer, and therefore 38 972 is not a square number.
The square of a number (here 38 972) is the result of the product of this number (38 972) by itself (i.e., 38 972 × 38 972); the square of 38 972 is sometimes called "raising 38 972 to the power 2", or "38 972 squared".
The square of 38 972 is 1 518 816 784 because 38 972 × 38 972 = 38 9722 = 1 518 816 784.
As a consequence, 38 972 is the square root of 1 518 816 784.
The multiples of 38 972 are all integers evenly divisible by 38 972, that is all numbers such that the remainder of the division by 38 972 is zero. There are infinitely many multiples of 38 972. The smallest multiples of 38 972 are: