It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 51 689 is not a prime number.
For example, 51 689 can be divided by 11: 51 689 / 11 = 4 699.
For 51 689 to be a prime number, it would have been required that 51 689 has only two divisors, i.e., itself and 1.
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51 689 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 51 689 is about 227.352.
Thus, the square root of 51 689 is not an integer, and therefore 51 689 is not a square number.
The square of a number (here 51 689) is the result of the product of this number (51 689) by itself (i.e., 51 689 × 51 689); the square of 51 689 is sometimes called "raising 51 689 to the power 2", or "51 689 squared".
The square of 51 689 is 2 671 752 721 because 51 689 × 51 689 = 51 6892 = 2 671 752 721.
As a consequence, 51 689 is the square root of 2 671 752 721.
The multiples of 51 689 are all integers evenly divisible by 51 689, that is all numbers such that the remainder of the division by 51 689 is zero. There are infinitely many multiples of 51 689. The smallest multiples of 51 689 are: