It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 233, the answer is: yes, 233 is a prime number because it has only two distinct divisors: 1 and itself (233).
As a consequence, 233 is only a multiple of 1 and 233..
Since 233 is a prime number, 233 is also a deficient number, that is to say 233 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 233 without 233 itself (that is 1, by definition!).
Parity of 233
233 is an odd number, because it is not evenly divisible by 2.
Is 233 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 233 is about 15.264.
Thus, the square root of 233 is not an integer, and therefore 233 is not a square number.
Anyway, 233 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 233?
The square of a number (here 233) is the result of the product of this number (233) by itself (i.e., 233 × 233); the square of 233 is sometimes called "raising 233 to the power 2", or "233 squared".
As a consequence, 233 is the square root of 54 289.
Number of digits of 233
233 is a number with 3 digits.
What are the multiples of 233?
The multiples of 233 are all integers evenly divisible by 233, that is all numbers such that the remainder of the division by 233 is zero. There are infinitely many multiples of 233. The smallest multiples of 233 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 233 too, since 0 × 233 = 0
- 233: indeed, 233 is a multiple of itself, since 233 is evenly divisible by 233 (we have 233 / 233 = 1, so the remainder of this division is indeed zero)
- 466: indeed, 466 = 233 × 2
- 699: indeed, 699 = 233 × 3
- 932: indeed, 932 = 233 × 4
- 1 165: indeed, 1 165 = 233 × 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 233). 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 15.264). 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.