It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 213 137 is not a prime number.
For example, 213 137 can be divided by 131: 213 137 / 131 = 1 627.
For 213 137 to be a prime number, it would have been required that 213 137 has only two divisors, i.e., itself and 1.
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213 137 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 213 137 is about 461.668.
Thus, the square root of 213 137 is not an integer, and therefore 213 137 is not a square number.
The square of a number (here 213 137) is the result of the product of this number (213 137) by itself (i.e., 213 137 × 213 137); the square of 213 137 is sometimes called "raising 213 137 to the power 2", or "213 137 squared".
The square of 213 137 is 45 427 380 769 because 213 137 × 213 137 = 213 1372 = 45 427 380 769.
As a consequence, 213 137 is the square root of 45 427 380 769.
The multiples of 213 137 are all integers evenly divisible by 213 137, that is all numbers such that the remainder of the division by 213 137 is zero. There are infinitely many multiples of 213 137. The smallest multiples of 213 137 are: