Is 389 a prime number?

389 is an odd number, because it is not evenly divisible by 2.

Find out more:

• What is an even 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.

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".

The square of 389 is 151 321 because 389 × 389 = 389² = 151 321.

As a consequence, 389 is the square root of 151 321.

389 is a number with 3 digits.

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
• etc.

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.

• Preceding numbers: …387, 388
• Following numbers: 390, 391…

Nearest numbers from 389

• Preceding prime number: 383
• Following prime number: 397

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• 389 est-il un nombre premier ?