It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 421 407 is not a prime number.
For example, 421 407 can be divided by 3: 421 407 / 3 = 140 469.
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For 421 407 to be a prime number, it would have been required that 421 407 has only two divisors, i.e., itself and 1.
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421 407 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 421 407 is about 649.159.
Thus, the square root of 421 407 is not an integer, and therefore 421 407 is not a square number.
The square of a number (here 421 407) is the result of the product of this number (421 407) by itself (i.e., 421 407 × 421 407); the square of 421 407 is sometimes called "raising 421 407 to the power 2", or "421 407 squared".
The square of 421 407 is 177 583 859 649 because 421 407 × 421 407 = 421 4072 = 177 583 859 649.
As a consequence, 421 407 is the square root of 177 583 859 649.
The multiples of 421 407 are all integers evenly divisible by 421 407, that is all numbers such that the remainder of the division by 421 407 is zero. There are infinitely many multiples of 421 407. The smallest multiples of 421 407 are: