It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 227, the answer is: yes, 227 is a prime number because it has only two distinct divisors: 1 and itself (227).
As a consequence, 227 is only a multiple of 1 and 227..
Since 227 is a prime number, 227 is also a deficient number, that is to say 227 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 227 without 227 itself (that is 1, by definition!).
Parity of 227
227 is an odd number, because it is not evenly divisible by 2.
Is 227 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 227 is about 15.067.
Thus, the square root of 227 is not an integer, and therefore 227 is not a square number.
Anyway, 227 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 227?
The square of a number (here 227) is the result of the product of this number (227) by itself (i.e., 227 × 227); the square of 227 is sometimes called "raising 227 to the power 2", or "227 squared".
As a consequence, 227 is the square root of 51 529.
Number of digits of 227
227 is a number with 3 digits.
What are the multiples of 227?
The multiples of 227 are all integers evenly divisible by 227, that is all numbers such that the remainder of the division by 227 is zero. There are infinitely many multiples of 227. The smallest multiples of 227 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 227 too, since 0 × 227 = 0
- 227: indeed, 227 is a multiple of itself, since 227 is evenly divisible by 227 (we have 227 / 227 = 1, so the remainder of this division is indeed zero)
- 454: indeed, 454 = 227 × 2
- 681: indeed, 681 = 227 × 3
- 908: indeed, 908 = 227 × 4
- 1 135: indeed, 1 135 = 227 × 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 227). 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 15.067). 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.