It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 680 684 is not a prime number.
For example, 680 684 can be divided by 2: 680 684 / 2 = 340 342.
For 680 684 to be a prime number, it would have been required that 680 684 has only two divisors, i.e., itself and 1.
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680 684 is an even number, because it is evenly divisible by 2: 680 684 / 2 = 340 342.
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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 680 684 is about 825.036.
Thus, the square root of 680 684 is not an integer, and therefore 680 684 is not a square number.
The square of a number (here 680 684) is the result of the product of this number (680 684) by itself (i.e., 680 684 × 680 684); the square of 680 684 is sometimes called "raising 680 684 to the power 2", or "680 684 squared".
The square of 680 684 is 463 330 707 856 because 680 684 × 680 684 = 680 6842 = 463 330 707 856.
As a consequence, 680 684 is the square root of 463 330 707 856.
The multiples of 680 684 are all integers evenly divisible by 680 684, that is all numbers such that the remainder of the division by 680 684 is zero. There are infinitely many multiples of 680 684. The smallest multiples of 680 684 are: