It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 229, the answer is: yes, 229 is a prime number because it has only two distinct divisors: 1 and itself (229).
As a consequence, 229 is only a multiple of 1 and 229..
Since 229 is a prime number, 229 is also a deficient number, that is to say 229 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 229 without 229 itself (that is 1, by definition!).
Parity of 229
229 is an odd number, because it is not evenly divisible by 2.
Is 229 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 229 is about 15.133.
Thus, the square root of 229 is not an integer, and therefore 229 is not a square number.
Anyway, 229 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 229?
The square of a number (here 229) is the result of the product of this number (229) by itself (i.e., 229 × 229); the square of 229 is sometimes called "raising 229 to the power 2", or "229 squared".
As a consequence, 229 is the square root of 52 441.
Number of digits of 229
229 is a number with 3 digits.
What are the multiples of 229?
The multiples of 229 are all integers evenly divisible by 229, that is all numbers such that the remainder of the division by 229 is zero. There are infinitely many multiples of 229. The smallest multiples of 229 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 229 too, since 0 × 229 = 0
- 229: indeed, 229 is a multiple of itself, since 229 is evenly divisible by 229 (we have 229 / 229 = 1, so the remainder of this division is indeed zero)
- 458: indeed, 458 = 229 × 2
- 687: indeed, 687 = 229 × 3
- 916: indeed, 916 = 229 × 4
- 1 145: indeed, 1 145 = 229 × 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 229). 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 15.133). 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.