It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 10 509 is not a prime number.
For example, 10 509 can be divided by 3: 10 509 / 3 = 3 503.
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For 10 509 to be a prime number, it would have been required that 10 509 has only two divisors, i.e., itself and 1.
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10 509 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 10 509 is about 102.513.
Thus, the square root of 10 509 is not an integer, and therefore 10 509 is not a square number.
The square of a number (here 10 509) is the result of the product of this number (10 509) by itself (i.e., 10 509 × 10 509); the square of 10 509 is sometimes called "raising 10 509 to the power 2", or "10 509 squared".
The square of 10 509 is 110 439 081 because 10 509 × 10 509 = 10 5092 = 110 439 081.
As a consequence, 10 509 is the square root of 110 439 081.
The multiples of 10 509 are all integers evenly divisible by 10 509, that is all numbers such that the remainder of the division by 10 509 is zero. There are infinitely many multiples of 10 509. The smallest multiples of 10 509 are: