It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 537 509 is not a prime number.
For example, 537 509 can be divided by 7: 537 509 / 7 = 76 787.
For 537 509 to be a prime number, it would have been required that 537 509 has only two divisors, i.e., itself and 1.
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537 509 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 537 509 is about 733.150.
Thus, the square root of 537 509 is not an integer, and therefore 537 509 is not a square number.
The square of a number (here 537 509) is the result of the product of this number (537 509) by itself (i.e., 537 509 × 537 509); the square of 537 509 is sometimes called "raising 537 509 to the power 2", or "537 509 squared".
The square of 537 509 is 288 915 925 081 because 537 509 × 537 509 = 537 5092 = 288 915 925 081.
As a consequence, 537 509 is the square root of 288 915 925 081.
The multiples of 537 509 are all integers evenly divisible by 537 509, that is all numbers such that the remainder of the division by 537 509 is zero. There are infinitely many multiples of 537 509. The smallest multiples of 537 509 are: