It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 013 is not a prime number.
For example, 138 013 can be divided by 79: 138 013 / 79 = 1 747.
For 138 013 to be a prime number, it would have been required that 138 013 has only two divisors, i.e., itself and 1.
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138 013 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 138 013 is about 371.501.
Thus, the square root of 138 013 is not an integer, and therefore 138 013 is not a square number.
The square of a number (here 138 013) is the result of the product of this number (138 013) by itself (i.e., 138 013 × 138 013); the square of 138 013 is sometimes called "raising 138 013 to the power 2", or "138 013 squared".
The square of 138 013 is 19 047 588 169 because 138 013 × 138 013 = 138 0132 = 19 047 588 169.
As a consequence, 138 013 is the square root of 19 047 588 169.
The multiples of 138 013 are all integers evenly divisible by 138 013, that is all numbers such that the remainder of the division by 138 013 is zero. There are infinitely many multiples of 138 013. The smallest multiples of 138 013 are: