It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 407 is not a prime number.
For example, 137 407 can be divided by 313: 137 407 / 313 = 439.
For 137 407 to be a prime number, it would have been required that 137 407 has only two divisors, i.e., itself and 1.
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137 407 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 137 407 is about 370.685.
Thus, the square root of 137 407 is not an integer, and therefore 137 407 is not a square number.
The square of a number (here 137 407) is the result of the product of this number (137 407) by itself (i.e., 137 407 × 137 407); the square of 137 407 is sometimes called "raising 137 407 to the power 2", or "137 407 squared".
The square of 137 407 is 18 880 683 649 because 137 407 × 137 407 = 137 4072 = 18 880 683 649.
As a consequence, 137 407 is the square root of 18 880 683 649.
The multiples of 137 407 are all integers evenly divisible by 137 407, that is all numbers such that the remainder of the division by 137 407 is zero. There are infinitely many multiples of 137 407. The smallest multiples of 137 407 are: