It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 223, the answer is: yes, 223 is a prime number because it has only two distinct divisors: 1 and itself (223).
As a consequence, 223 is only a multiple of 1 and 223..
Since 223 is a prime number, 223 is also a deficient number, that is to say 223 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 223 without 223 itself (that is 1, by definition!).
Parity of 223
223 is an odd number, because it is not evenly divisible by 2.
Is 223 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 223 is about 14.933.
Thus, the square root of 223 is not an integer, and therefore 223 is not a square number.
Anyway, 223 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 223?
The square of a number (here 223) is the result of the product of this number (223) by itself (i.e., 223 × 223); the square of 223 is sometimes called "raising 223 to the power 2", or "223 squared".
As a consequence, 223 is the square root of 49 729.
Number of digits of 223
223 is a number with 3 digits.
What are the multiples of 223?
The multiples of 223 are all integers evenly divisible by 223, that is all numbers such that the remainder of the division by 223 is zero. There are infinitely many multiples of 223. The smallest multiples of 223 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 223 too, since 0 × 223 = 0
- 223: indeed, 223 is a multiple of itself, since 223 is evenly divisible by 223 (we have 223 / 223 = 1, so the remainder of this division is indeed zero)
- 446: indeed, 446 = 223 × 2
- 669: indeed, 669 = 223 × 3
- 892: indeed, 892 = 223 × 4
- 1 115: indeed, 1 115 = 223 × 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 223). 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 14.933). 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.