It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 421 509 is not a prime number.
For example, 421 509 can be divided by 3: 421 509 / 3 = 140 503.
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For 421 509 to be a prime number, it would have been required that 421 509 has only two divisors, i.e., itself and 1.
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421 509 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 421 509 is about 649.237.
Thus, the square root of 421 509 is not an integer, and therefore 421 509 is not a square number.
The square of a number (here 421 509) is the result of the product of this number (421 509) by itself (i.e., 421 509 × 421 509); the square of 421 509 is sometimes called "raising 421 509 to the power 2", or "421 509 squared".
The square of 421 509 is 177 669 837 081 because 421 509 × 421 509 = 421 5092 = 177 669 837 081.
As a consequence, 421 509 is the square root of 177 669 837 081.
The multiples of 421 509 are all integers evenly divisible by 421 509, that is all numbers such that the remainder of the division by 421 509 is zero. There are infinitely many multiples of 421 509. The smallest multiples of 421 509 are: