It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 233 is not a prime number.
For example, 137 233 can be divided by 37: 137 233 / 37 = 3 709.
For 137 233 to be a prime number, it would have been required that 137 233 has only two divisors, i.e., itself and 1.
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137 233 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 137 233 is about 370.450.
Thus, the square root of 137 233 is not an integer, and therefore 137 233 is not a square number.
The square of a number (here 137 233) is the result of the product of this number (137 233) by itself (i.e., 137 233 × 137 233); the square of 137 233 is sometimes called "raising 137 233 to the power 2", or "137 233 squared".
The square of 137 233 is 18 832 896 289 because 137 233 × 137 233 = 137 2332 = 18 832 896 289.
As a consequence, 137 233 is the square root of 18 832 896 289.
The multiples of 137 233 are all integers evenly divisible by 137 233, that is all numbers such that the remainder of the division by 137 233 is zero. There are infinitely many multiples of 137 233. The smallest multiples of 137 233 are: