It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 414 427 is not a prime number.
For example, 414 427 can be divided by 13: 414 427 / 13 = 31 879.
For 414 427 to be a prime number, it would have been required that 414 427 has only two divisors, i.e., itself and 1.
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414 427 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 414 427 is about 643.760.
Thus, the square root of 414 427 is not an integer, and therefore 414 427 is not a square number.
The square of a number (here 414 427) is the result of the product of this number (414 427) by itself (i.e., 414 427 × 414 427); the square of 414 427 is sometimes called "raising 414 427 to the power 2", or "414 427 squared".
The square of 414 427 is 171 749 738 329 because 414 427 × 414 427 = 414 4272 = 171 749 738 329.
As a consequence, 414 427 is the square root of 171 749 738 329.
The multiples of 414 427 are all integers evenly divisible by 414 427, that is all numbers such that the remainder of the division by 414 427 is zero. There are infinitely many multiples of 414 427. The smallest multiples of 414 427 are: