It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 7 638 977 is not a prime number.
For example, 7 638 977 can be divided by 29: 7 638 977 / 29 = 263 413.
For 7 638 977 to be a prime number, it would have been required that 7 638 977 has only two divisors, i.e., itself and 1.
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7 638 977 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 7 638 977 is about 2 763.870.
Thus, the square root of 7 638 977 is not an integer, and therefore 7 638 977 is not a square number.
The square of a number (here 7 638 977) is the result of the product of this number (7 638 977) by itself (i.e., 7 638 977 × 7 638 977); the square of 7 638 977 is sometimes called "raising 7 638 977 to the power 2", or "7 638 977 squared".
The square of 7 638 977 is 58 353 969 606 529 because 7 638 977 × 7 638 977 = 7 638 9772 = 58 353 969 606 529.
As a consequence, 7 638 977 is the square root of 58 353 969 606 529.
The multiples of 7 638 977 are all integers evenly divisible by 7 638 977, that is all numbers such that the remainder of the division by 7 638 977 is zero. There are infinitely many multiples of 7 638 977. The smallest multiples of 7 638 977 are: