It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 439, the answer is: yes, 439 is a prime number because it has only two distinct divisors: 1 and itself (439).
As a consequence, 439 is only a multiple of 1 and 439..
Since 439 is a prime number, 439 is also a deficient number, that is to say 439 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 439 without 439 itself (that is 1, by definition!).
Parity of 439
439 is an odd number, because it is not evenly divisible by 2.
Is 439 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 439 is about 20.952.
Thus, the square root of 439 is not an integer, and therefore 439 is not a square number.
Anyway, 439 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 439?
The square of a number (here 439) is the result of the product of this number (439) by itself (i.e., 439 × 439); the square of 439 is sometimes called "raising 439 to the power 2", or "439 squared".
As a consequence, 439 is the square root of 192 721.
Number of digits of 439
439 is a number with 3 digits.
What are the multiples of 439?
The multiples of 439 are all integers evenly divisible by 439, that is all numbers such that the remainder of the division by 439 is zero. There are infinitely many multiples of 439. The smallest multiples of 439 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 439 too, since 0 × 439 = 0
- 439: indeed, 439 is a multiple of itself, since 439 is evenly divisible by 439 (we have 439 / 439 = 1, so the remainder of this division is indeed zero)
- 878: indeed, 878 = 439 × 2
- 1 317: indeed, 1 317 = 439 × 3
- 1 756: indeed, 1 756 = 439 × 4
- 2 195: indeed, 2 195 = 439 × 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 439). 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 20.952). 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.