It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 317 is not a prime number.
For example, 138 317 can be divided by 157: 138 317 / 157 = 881.
For 138 317 to be a prime number, it would have been required that 138 317 has only two divisors, i.e., itself and 1.
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138 317 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 138 317 is about 371.910.
Thus, the square root of 138 317 is not an integer, and therefore 138 317 is not a square number.
The square of a number (here 138 317) is the result of the product of this number (138 317) by itself (i.e., 138 317 × 138 317); the square of 138 317 is sometimes called "raising 138 317 to the power 2", or "138 317 squared".
The square of 138 317 is 19 131 592 489 because 138 317 × 138 317 = 138 3172 = 19 131 592 489.
As a consequence, 138 317 is the square root of 19 131 592 489.
The multiples of 138 317 are all integers evenly divisible by 138 317, that is all numbers such that the remainder of the division by 138 317 is zero. There are infinitely many multiples of 138 317. The smallest multiples of 138 317 are: