It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 443, the answer is: yes, 443 is a prime number because it has only two distinct divisors: 1 and itself (443).
As a consequence, 443 is only a multiple of 1 and 443..
Since 443 is a prime number, 443 is also a deficient number, that is to say 443 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 443 without 443 itself (that is 1, by definition!).
Parity of 443
443 is an odd number, because it is not evenly divisible by 2.
Is 443 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 443 is about 21.048.
Thus, the square root of 443 is not an integer, and therefore 443 is not a square number.
Anyway, 443 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 443?
The square of a number (here 443) is the result of the product of this number (443) by itself (i.e., 443 × 443); the square of 443 is sometimes called "raising 443 to the power 2", or "443 squared".
As a consequence, 443 is the square root of 196 249.
Number of digits of 443
443 is a number with 3 digits.
What are the multiples of 443?
The multiples of 443 are all integers evenly divisible by 443, that is all numbers such that the remainder of the division by 443 is zero. There are infinitely many multiples of 443. The smallest multiples of 443 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 443 too, since 0 × 443 = 0
- 443: indeed, 443 is a multiple of itself, since 443 is evenly divisible by 443 (we have 443 / 443 = 1, so the remainder of this division is indeed zero)
- 886: indeed, 886 = 443 × 2
- 1 329: indeed, 1 329 = 443 × 3
- 1 772: indeed, 1 772 = 443 × 4
- 2 215: indeed, 2 215 = 443 × 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 443). 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 21.048). 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.