It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 113 is not a prime number.
For example, 137 113 can be divided by 31: 137 113 / 31 = 4 423.
For 137 113 to be a prime number, it would have been required that 137 113 has only two divisors, i.e., itself and 1.
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137 113 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 137 113 is about 370.288.
Thus, the square root of 137 113 is not an integer, and therefore 137 113 is not a square number.
The square of a number (here 137 113) is the result of the product of this number (137 113) by itself (i.e., 137 113 × 137 113); the square of 137 113 is sometimes called "raising 137 113 to the power 2", or "137 113 squared".
The square of 137 113 is 18 799 974 769 because 137 113 × 137 113 = 137 1132 = 18 799 974 769.
As a consequence, 137 113 is the square root of 18 799 974 769.
The multiples of 137 113 are all integers evenly divisible by 137 113, that is all numbers such that the remainder of the division by 137 113 is zero. There are infinitely many multiples of 137 113. The smallest multiples of 137 113 are: