It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 638 is not a prime number.
For example, 137 638 can be divided by 2: 137 638 / 2 = 68 819.
For 137 638 to be a prime number, it would have been required that 137 638 has only two divisors, i.e., itself and 1.
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137 638 is an even number, because it is evenly divisible by 2: 137 638 / 2 = 68 819.
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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 137 638 is about 370.996.
Thus, the square root of 137 638 is not an integer, and therefore 137 638 is not a square number.
The square of a number (here 137 638) is the result of the product of this number (137 638) by itself (i.e., 137 638 × 137 638); the square of 137 638 is sometimes called "raising 137 638 to the power 2", or "137 638 squared".
The square of 137 638 is 18 944 219 044 because 137 638 × 137 638 = 137 6382 = 18 944 219 044.
As a consequence, 137 638 is the square root of 18 944 219 044.
The multiples of 137 638 are all integers evenly divisible by 137 638, that is all numbers such that the remainder of the division by 137 638 is zero. There are infinitely many multiples of 137 638. The smallest multiples of 137 638 are: