It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 513 is not a prime number.
For example, 138 513 can be divided by 3: 138 513 / 3 = 46 171.
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For 138 513 to be a prime number, it would have been required that 138 513 has only two divisors, i.e., itself and 1.
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138 513 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 138 513 is about 372.173.
Thus, the square root of 138 513 is not an integer, and therefore 138 513 is not a square number.
The square of a number (here 138 513) is the result of the product of this number (138 513) by itself (i.e., 138 513 × 138 513); the square of 138 513 is sometimes called "raising 138 513 to the power 2", or "138 513 squared".
The square of 138 513 is 19 185 851 169 because 138 513 × 138 513 = 138 5132 = 19 185 851 169.
As a consequence, 138 513 is the square root of 19 185 851 169.
The multiples of 138 513 are all integers evenly divisible by 138 513, that is all numbers such that the remainder of the division by 138 513 is zero. There are infinitely many multiples of 138 513. The smallest multiples of 138 513 are: