It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 212 137 is not a prime number.
For example, 212 137 can be divided by 307: 212 137 / 307 = 691.
For 212 137 to be a prime number, it would have been required that 212 137 has only two divisors, i.e., itself and 1.
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212 137 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 212 137 is about 460.583.
Thus, the square root of 212 137 is not an integer, and therefore 212 137 is not a square number.
The square of a number (here 212 137) is the result of the product of this number (212 137) by itself (i.e., 212 137 × 212 137); the square of 212 137 is sometimes called "raising 212 137 to the power 2", or "212 137 squared".
The square of 212 137 is 45 002 106 769 because 212 137 × 212 137 = 212 1372 = 45 002 106 769.
As a consequence, 212 137 is the square root of 45 002 106 769.
The multiples of 212 137 are all integers evenly divisible by 212 137, that is all numbers such that the remainder of the division by 212 137 is zero. There are infinitely many multiples of 212 137. The smallest multiples of 212 137 are: