It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 413 is not a prime number.
For example, 138 413 can be divided by 11: 138 413 / 11 = 12 583.
For 138 413 to be a prime number, it would have been required that 138 413 has only two divisors, i.e., itself and 1.
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138 413 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 138 413 is about 372.039.
Thus, the square root of 138 413 is not an integer, and therefore 138 413 is not a square number.
The square of a number (here 138 413) is the result of the product of this number (138 413) by itself (i.e., 138 413 × 138 413); the square of 138 413 is sometimes called "raising 138 413 to the power 2", or "138 413 squared".
The square of 138 413 is 19 158 158 569 because 138 413 × 138 413 = 138 4132 = 19 158 158 569.
As a consequence, 138 413 is the square root of 19 158 158 569.
The multiples of 138 413 are all integers evenly divisible by 138 413, that is all numbers such that the remainder of the division by 138 413 is zero. There are infinitely many multiples of 138 413. The smallest multiples of 138 413 are: