It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 813 is not a prime number.
For example, 137 813 can be divided by 13: 137 813 / 13 = 10 601.
For 137 813 to be a prime number, it would have been required that 137 813 has only two divisors, i.e., itself and 1.
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137 813 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 137 813 is about 371.232.
Thus, the square root of 137 813 is not an integer, and therefore 137 813 is not a square number.
The square of a number (here 137 813) is the result of the product of this number (137 813) by itself (i.e., 137 813 × 137 813); the square of 137 813 is sometimes called "raising 137 813 to the power 2", or "137 813 squared".
The square of 137 813 is 18 992 422 969 because 137 813 × 137 813 = 137 8132 = 18 992 422 969.
As a consequence, 137 813 is the square root of 18 992 422 969.
The multiples of 137 813 are all integers evenly divisible by 137 813, that is all numbers such that the remainder of the division by 137 813 is zero. There are infinitely many multiples of 137 813. The smallest multiples of 137 813 are: