It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 463 401 is not a prime number.
For example, 463 401 can be divided by 3: 463 401 / 3 = 154 467.
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For 463 401 to be a prime number, it would have been required that 463 401 has only two divisors, i.e., itself and 1.
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463 401 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 463 401 is about 680.736.
Thus, the square root of 463 401 is not an integer, and therefore 463 401 is not a square number.
The square of a number (here 463 401) is the result of the product of this number (463 401) by itself (i.e., 463 401 × 463 401); the square of 463 401 is sometimes called "raising 463 401 to the power 2", or "463 401 squared".
The square of 463 401 is 214 740 486 801 because 463 401 × 463 401 = 463 4012 = 214 740 486 801.
As a consequence, 463 401 is the square root of 214 740 486 801.
The multiples of 463 401 are all integers evenly divisible by 463 401, that is all numbers such that the remainder of the division by 463 401 is zero. There are infinitely many multiples of 463 401. The smallest multiples of 463 401 are: