It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 389, the answer is: yes, 389 is a prime number because it has only two distinct divisors: 1 and itself (389).
As a consequence, 389 is only a multiple of 1 and 389..
Since 389 is a prime number, 389 is also a deficient number, that is to say 389 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 389 without 389 itself (that is 1, by definition!).
Parity of 389
389 is an odd number, because it is not evenly divisible by 2.
Is 389 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 389 is about 19.723.
Thus, the square root of 389 is not an integer, and therefore 389 is not a square number.
Anyway, 389 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 389?
The square of a number (here 389) is the result of the product of this number (389) by itself (i.e., 389 × 389); the square of 389 is sometimes called "raising 389 to the power 2", or "389 squared".
As a consequence, 389 is the square root of 151 321.
Number of digits of 389
389 is a number with 3 digits.
What are the multiples of 389?
The multiples of 389 are all integers evenly divisible by 389, that is all numbers such that the remainder of the division by 389 is zero. There are infinitely many multiples of 389. The smallest multiples of 389 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 389 too, since 0 × 389 = 0
- 389: indeed, 389 is a multiple of itself, since 389 is evenly divisible by 389 (we have 389 / 389 = 1, so the remainder of this division is indeed zero)
- 778: indeed, 778 = 389 × 2
- 1 167: indeed, 1 167 = 389 × 3
- 1 556: indeed, 1 556 = 389 × 4
- 1 945: indeed, 1 945 = 389 × 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 389). 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 19.723). 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.