It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 564 is not a prime number.
For example, 137 564 can be divided by 2: 137 564 / 2 = 68 782.
For 137 564 to be a prime number, it would have been required that 137 564 has only two divisors, i.e., itself and 1.
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137 564 is an even number, because it is evenly divisible by 2: 137 564 / 2 = 68 782.
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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 137 564 is about 370.896.
Thus, the square root of 137 564 is not an integer, and therefore 137 564 is not a square number.
The square of a number (here 137 564) is the result of the product of this number (137 564) by itself (i.e., 137 564 × 137 564); the square of 137 564 is sometimes called "raising 137 564 to the power 2", or "137 564 squared".
The square of 137 564 is 18 923 854 096 because 137 564 × 137 564 = 137 5642 = 18 923 854 096.
As a consequence, 137 564 is the square root of 18 923 854 096.
The multiples of 137 564 are all integers evenly divisible by 137 564, that is all numbers such that the remainder of the division by 137 564 is zero. There are infinitely many multiples of 137 564. The smallest multiples of 137 564 are: