It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 643, the answer is: yes, 643 is a prime number because it has only two distinct divisors: 1 and itself (643).
As a consequence, 643 is only a multiple of 1 and 643..
Since 643 is a prime number, 643 is also a deficient number, that is to say 643 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 643 without 643 itself (that is 1, by definition!).
Parity of 643
643 is an odd number, because it is not evenly divisible by 2.
Is 643 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 643 is about 25.357.
Thus, the square root of 643 is not an integer, and therefore 643 is not a square number.
Anyway, 643 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 643?
The square of a number (here 643) is the result of the product of this number (643) by itself (i.e., 643 × 643); the square of 643 is sometimes called "raising 643 to the power 2", or "643 squared".
As a consequence, 643 is the square root of 413 449.
Number of digits of 643
643 is a number with 3 digits.
What are the multiples of 643?
The multiples of 643 are all integers evenly divisible by 643, that is all numbers such that the remainder of the division by 643 is zero. There are infinitely many multiples of 643. The smallest multiples of 643 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 643 too, since 0 × 643 = 0
- 643: indeed, 643 is a multiple of itself, since 643 is evenly divisible by 643 (we have 643 / 643 = 1, so the remainder of this division is indeed zero)
- 1 286: indeed, 1 286 = 643 × 2
- 1 929: indeed, 1 929 = 643 × 3
- 2 572: indeed, 2 572 = 643 × 4
- 3 215: indeed, 3 215 = 643 × 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 643). 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 25.357). 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.