It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 1 009 821 is not a prime number.
For example, 1 009 821 can be divided by 3: 1 009 821 / 3 = 336 607.
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For 1 009 821 to be a prime number, it would have been required that 1 009 821 has only two divisors, i.e., itself and 1.
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1 009 821 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 1 009 821 is about 1 004.899.
Thus, the square root of 1 009 821 is not an integer, and therefore 1 009 821 is not a square number.
The square of a number (here 1 009 821) is the result of the product of this number (1 009 821) by itself (i.e., 1 009 821 × 1 009 821); the square of 1 009 821 is sometimes called "raising 1 009 821 to the power 2", or "1 009 821 squared".
The square of 1 009 821 is 1 019 738 452 041 because 1 009 821 × 1 009 821 = 1 009 8212 = 1 019 738 452 041.
As a consequence, 1 009 821 is the square root of 1 019 738 452 041.
The multiples of 1 009 821 are all integers evenly divisible by 1 009 821, that is all numbers such that the remainder of the division by 1 009 821 is zero. There are infinitely many multiples of 1 009 821. The smallest multiples of 1 009 821 are: