It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 433, the answer is: yes, 433 is a prime number because it has only two distinct divisors: 1 and itself (433).
As a consequence, 433 is only a multiple of 1 and 433..
Since 433 is a prime number, 433 is also a deficient number, that is to say 433 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 433 without 433 itself (that is 1, by definition!).
Parity of 433
433 is an odd number, because it is not evenly divisible by 2.
Is 433 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 433 is about 20.809.
Thus, the square root of 433 is not an integer, and therefore 433 is not a square number.
Anyway, 433 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 433?
The square of a number (here 433) is the result of the product of this number (433) by itself (i.e., 433 × 433); the square of 433 is sometimes called "raising 433 to the power 2", or "433 squared".
As a consequence, 433 is the square root of 187 489.
Number of digits of 433
433 is a number with 3 digits.
What are the multiples of 433?
The multiples of 433 are all integers evenly divisible by 433, that is all numbers such that the remainder of the division by 433 is zero. There are infinitely many multiples of 433. The smallest multiples of 433 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 433 too, since 0 × 433 = 0
- 433: indeed, 433 is a multiple of itself, since 433 is evenly divisible by 433 (we have 433 / 433 = 1, so the remainder of this division is indeed zero)
- 866: indeed, 866 = 433 × 2
- 1 299: indeed, 1 299 = 433 × 3
- 1 732: indeed, 1 732 = 433 × 4
- 2 165: indeed, 2 165 = 433 × 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 433). 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 20.809). 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.