It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 197 193 is not a prime number.
For example, 197 193 can be divided by 3: 197 193 / 3 = 65 731.
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For 197 193 to be a prime number, it would have been required that 197 193 has only two divisors, i.e., itself and 1.
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197 193 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 197 193 is about 444.064.
Thus, the square root of 197 193 is not an integer, and therefore 197 193 is not a square number.
The square of a number (here 197 193) is the result of the product of this number (197 193) by itself (i.e., 197 193 × 197 193); the square of 197 193 is sometimes called "raising 197 193 to the power 2", or "197 193 squared".
The square of 197 193 is 38 885 079 249 because 197 193 × 197 193 = 197 1932 = 38 885 079 249.
As a consequence, 197 193 is the square root of 38 885 079 249.
The multiples of 197 193 are all integers evenly divisible by 197 193, that is all numbers such that the remainder of the division by 197 193 is zero. There are infinitely many multiples of 197 193. The smallest multiples of 197 193 are: