It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 683, the answer is: yes, 683 is a prime number because it has only two distinct divisors: 1 and itself (683).
As a consequence, 683 is only a multiple of 1 and 683..
Since 683 is a prime number, 683 is also a deficient number, that is to say 683 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 683 without 683 itself (that is 1, by definition!).
Parity of 683
683 is an odd number, because it is not evenly divisible by 2.
Is 683 a perfect square number?
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 683 is about 26.134.
Thus, the square root of 683 is not an integer, and therefore 683 is not a square number.
Anyway, 683 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 683?
The square of a number (here 683) is the result of the product of this number (683) by itself (i.e., 683 × 683); the square of 683 is sometimes called "raising 683 to the power 2", or "683 squared".
As a consequence, 683 is the square root of 466 489.
Number of digits of 683
683 is a number with 3 digits.
What are the multiples of 683?
The multiples of 683 are all integers evenly divisible by 683, that is all numbers such that the remainder of the division by 683 is zero. There are infinitely many multiples of 683. The smallest multiples of 683 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 683 too, since 0 × 683 = 0
- 683: indeed, 683 is a multiple of itself, since 683 is evenly divisible by 683 (we have 683 / 683 = 1, so the remainder of this division is indeed zero)
- 1 366: indeed, 1 366 = 683 × 2
- 2 049: indeed, 2 049 = 683 × 3
- 2 732: indeed, 2 732 = 683 × 4
- 3 415: indeed, 3 415 = 683 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 683). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 26.134). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.