It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 7 638 397 is not a prime number.
For example, 7 638 397 can be divided by 13: 7 638 397 / 13 = 587 569.
For 7 638 397 to be a prime number, it would have been required that 7 638 397 has only two divisors, i.e., itself and 1.
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7 638 397 is an odd number, because it is not evenly divisible by 2.
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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 7 638 397 is about 2 763.765.
Thus, the square root of 7 638 397 is not an integer, and therefore 7 638 397 is not a square number.
The square of a number (here 7 638 397) is the result of the product of this number (7 638 397) by itself (i.e., 7 638 397 × 7 638 397); the square of 7 638 397 is sometimes called "raising 7 638 397 to the power 2", or "7 638 397 squared".
The square of 7 638 397 is 58 345 108 729 609 because 7 638 397 × 7 638 397 = 7 638 3972 = 58 345 108 729 609.
As a consequence, 7 638 397 is the square root of 58 345 108 729 609.
The multiples of 7 638 397 are all integers evenly divisible by 7 638 397, that is all numbers such that the remainder of the division by 7 638 397 is zero. There are infinitely many multiples of 7 638 397. The smallest multiples of 7 638 397 are: