It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 138 is not a prime number.
For example, 5 138 can be divided by 2: 5 138 / 2 = 2 569.
For 5 138 to be a prime number, it would have been required that 5 138 has only two divisors, i.e., itself and 1.
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5 138 is an even number, because it is evenly divisible by 2: 5 138 / 2 = 2 569.
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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 5 138 is about 71.680.
Thus, the square root of 5 138 is not an integer, and therefore 5 138 is not a square number.
The square of a number (here 5 138) is the result of the product of this number (5 138) by itself (i.e., 5 138 × 5 138); the square of 5 138 is sometimes called "raising 5 138 to the power 2", or "5 138 squared".
The square of 5 138 is 26 399 044 because 5 138 × 5 138 = 5 1382 = 26 399 044.
As a consequence, 5 138 is the square root of 26 399 044.
The multiples of 5 138 are all integers evenly divisible by 5 138, that is all numbers such that the remainder of the division by 5 138 is zero. There are infinitely many multiples of 5 138. The smallest multiples of 5 138 are: