It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 165 401 is not a prime number.
For example, 165 401 can be divided by 193: 165 401 / 193 = 857.
For 165 401 to be a prime number, it would have been required that 165 401 has only two divisors, i.e., itself and 1.
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165 401 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 165 401 is about 406.695.
Thus, the square root of 165 401 is not an integer, and therefore 165 401 is not a square number.
The square of a number (here 165 401) is the result of the product of this number (165 401) by itself (i.e., 165 401 × 165 401); the square of 165 401 is sometimes called "raising 165 401 to the power 2", or "165 401 squared".
The square of 165 401 is 27 357 490 801 because 165 401 × 165 401 = 165 4012 = 27 357 490 801.
As a consequence, 165 401 is the square root of 27 357 490 801.
The multiples of 165 401 are all integers evenly divisible by 165 401, that is all numbers such that the remainder of the division by 165 401 is zero. There are infinitely many multiples of 165 401. The smallest multiples of 165 401 are: