It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 101 509 is not a prime number.
For example, 101 509 can be divided by 83: 101 509 / 83 = 1 223.
For 101 509 to be a prime number, it would have been required that 101 509 has only two divisors, i.e., itself and 1.
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101 509 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 101 509 is about 318.605.
Thus, the square root of 101 509 is not an integer, and therefore 101 509 is not a square number.
The square of a number (here 101 509) is the result of the product of this number (101 509) by itself (i.e., 101 509 × 101 509); the square of 101 509 is sometimes called "raising 101 509 to the power 2", or "101 509 squared".
The square of 101 509 is 10 304 077 081 because 101 509 × 101 509 = 101 5092 = 10 304 077 081.
As a consequence, 101 509 is the square root of 10 304 077 081.
The multiples of 101 509 are all integers evenly divisible by 101 509, that is all numbers such that the remainder of the division by 101 509 is zero. There are infinitely many multiples of 101 509. The smallest multiples of 101 509 are: