It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 138 is not a prime number.
For example, 137 138 can be divided by 2: 137 138 / 2 = 68 569.
For 137 138 to be a prime number, it would have been required that 137 138 has only two divisors, i.e., itself and 1.
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137 138 is an even number, because it is evenly divisible by 2: 137 138 / 2 = 68 569.
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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 137 138 is about 370.321.
Thus, the square root of 137 138 is not an integer, and therefore 137 138 is not a square number.
The square of a number (here 137 138) is the result of the product of this number (137 138) by itself (i.e., 137 138 × 137 138); the square of 137 138 is sometimes called "raising 137 138 to the power 2", or "137 138 squared".
The square of 137 138 is 18 806 831 044 because 137 138 × 137 138 = 137 1382 = 18 806 831 044.
As a consequence, 137 138 is the square root of 18 806 831 044.
The multiples of 137 138 are all integers evenly divisible by 137 138, that is all numbers such that the remainder of the division by 137 138 is zero. There are infinitely many multiples of 137 138. The smallest multiples of 137 138 are: