It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 509 is not a prime number.
For example, 138 509 can be divided by 7: 138 509 / 7 = 19 787.
For 138 509 to be a prime number, it would have been required that 138 509 has only two divisors, i.e., itself and 1.
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138 509 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 138 509 is about 372.168.
Thus, the square root of 138 509 is not an integer, and therefore 138 509 is not a square number.
The square of a number (here 138 509) is the result of the product of this number (138 509) by itself (i.e., 138 509 × 138 509); the square of 138 509 is sometimes called "raising 138 509 to the power 2", or "138 509 squared".
The square of 138 509 is 19 184 743 081 because 138 509 × 138 509 = 138 5092 = 19 184 743 081.
As a consequence, 138 509 is the square root of 19 184 743 081.
The multiples of 138 509 are all integers evenly divisible by 138 509, that is all numbers such that the remainder of the division by 138 509 is zero. There are infinitely many multiples of 138 509. The smallest multiples of 138 509 are: