It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 217 is not a prime number.
For example, 138 217 can be divided by 89: 138 217 / 89 = 1 553.
For 138 217 to be a prime number, it would have been required that 138 217 has only two divisors, i.e., itself and 1.
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138 217 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 138 217 is about 371.775.
Thus, the square root of 138 217 is not an integer, and therefore 138 217 is not a square number.
The square of a number (here 138 217) is the result of the product of this number (138 217) by itself (i.e., 138 217 × 138 217); the square of 138 217 is sometimes called "raising 138 217 to the power 2", or "138 217 squared".
The square of 138 217 is 19 103 939 089 because 138 217 × 138 217 = 138 2172 = 19 103 939 089.
As a consequence, 138 217 is the square root of 19 103 939 089.
The multiples of 138 217 are all integers evenly divisible by 138 217, that is all numbers such that the remainder of the division by 138 217 is zero. There are infinitely many multiples of 138 217. The smallest multiples of 138 217 are: