It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 523 is not a prime number.
For example, 137 523 can be divided by 3: 137 523 / 3 = 45 841.
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For 137 523 to be a prime number, it would have been required that 137 523 has only two divisors, i.e., itself and 1.
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137 523 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 137 523 is about 370.841.
Thus, the square root of 137 523 is not an integer, and therefore 137 523 is not a square number.
The square of a number (here 137 523) is the result of the product of this number (137 523) by itself (i.e., 137 523 × 137 523); the square of 137 523 is sometimes called "raising 137 523 to the power 2", or "137 523 squared".
The square of 137 523 is 18 912 575 529 because 137 523 × 137 523 = 137 5232 = 18 912 575 529.
As a consequence, 137 523 is the square root of 18 912 575 529.
The multiples of 137 523 are all integers evenly divisible by 137 523, that is all numbers such that the remainder of the division by 137 523 is zero. There are infinitely many multiples of 137 523. The smallest multiples of 137 523 are: