It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 723 689 is not a prime number.
For example, 723 689 can be divided by 641: 723 689 / 641 = 1 129.
For 723 689 to be a prime number, it would have been required that 723 689 has only two divisors, i.e., itself and 1.
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723 689 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 723 689 is about 850.699.
Thus, the square root of 723 689 is not an integer, and therefore 723 689 is not a square number.
The square of a number (here 723 689) is the result of the product of this number (723 689) by itself (i.e., 723 689 × 723 689); the square of 723 689 is sometimes called "raising 723 689 to the power 2", or "723 689 squared".
The square of 723 689 is 523 725 768 721 because 723 689 × 723 689 = 723 6892 = 523 725 768 721.
As a consequence, 723 689 is the square root of 523 725 768 721.
The multiples of 723 689 are all integers evenly divisible by 723 689, that is all numbers such that the remainder of the division by 723 689 is zero. There are infinitely many multiples of 723 689. The smallest multiples of 723 689 are: