It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 239, the answer is: yes, 239 is a prime number because it has only two distinct divisors: 1 and itself (239).
As a consequence, 239 is only a multiple of 1 and 239..
Since 239 is a prime number, 239 is also a deficient number, that is to say 239 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 239 without 239 itself (that is 1, by definition!).
Parity of 239
239 is an odd number, because it is not evenly divisible by 2.
Is 239 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 239 is about 15.460.
Thus, the square root of 239 is not an integer, and therefore 239 is not a square number.
Anyway, 239 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 239?
The square of a number (here 239) is the result of the product of this number (239) by itself (i.e., 239 × 239); the square of 239 is sometimes called "raising 239 to the power 2", or "239 squared".
As a consequence, 239 is the square root of 57 121.
Number of digits of 239
239 is a number with 3 digits.
What are the multiples of 239?
The multiples of 239 are all integers evenly divisible by 239, that is all numbers such that the remainder of the division by 239 is zero. There are infinitely many multiples of 239. The smallest multiples of 239 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 239 too, since 0 × 239 = 0
- 239: indeed, 239 is a multiple of itself, since 239 is evenly divisible by 239 (we have 239 / 239 = 1, so the remainder of this division is indeed zero)
- 478: indeed, 478 = 239 × 2
- 717: indeed, 717 = 239 × 3
- 956: indeed, 956 = 239 × 4
- 1 195: indeed, 1 195 = 239 × 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 239). 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 15.460). 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.