It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 421 401 is not a prime number.
For example, 421 401 can be divided by 3: 421 401 / 3 = 140 467.
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For 421 401 to be a prime number, it would have been required that 421 401 has only two divisors, i.e., itself and 1.
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421 401 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 421 401 is about 649.154.
Thus, the square root of 421 401 is not an integer, and therefore 421 401 is not a square number.
The square of a number (here 421 401) is the result of the product of this number (421 401) by itself (i.e., 421 401 × 421 401); the square of 421 401 is sometimes called "raising 421 401 to the power 2", or "421 401 squared".
The square of 421 401 is 177 578 802 801 because 421 401 × 421 401 = 421 4012 = 177 578 802 801.
As a consequence, 421 401 is the square root of 177 578 802 801.
The multiples of 421 401 are all integers evenly divisible by 421 401, that is all numbers such that the remainder of the division by 421 401 is zero. There are infinitely many multiples of 421 401. The smallest multiples of 421 401 are: