It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 51 509 is not a prime number.
For example, 51 509 can be divided by 19: 51 509 / 19 = 2 711.
For 51 509 to be a prime number, it would have been required that 51 509 has only two divisors, i.e., itself and 1.
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51 509 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 51 509 is about 226.956.
Thus, the square root of 51 509 is not an integer, and therefore 51 509 is not a square number.
The square of a number (here 51 509) is the result of the product of this number (51 509) by itself (i.e., 51 509 × 51 509); the square of 51 509 is sometimes called "raising 51 509 to the power 2", or "51 509 squared".
The square of 51 509 is 2 653 177 081 because 51 509 × 51 509 = 51 5092 = 2 653 177 081.
As a consequence, 51 509 is the square root of 2 653 177 081.
The multiples of 51 509 are all integers evenly divisible by 51 509, that is all numbers such that the remainder of the division by 51 509 is zero. There are infinitely many multiples of 51 509. The smallest multiples of 51 509 are: