Is 399 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 399, the answer is: No, 399 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 399) is as follows: 1, 3, 7, 19, 21, 57, 133, 399.

For 399 to be a prime number, it would have been required that 399 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

399 is a multiple of 1
399 is a multiple of 3
399 is a multiple of 7
399 is a multiple of 19
399 is a multiple of 21
399 is a multiple of 57
399 is a multiple of 133

For 399 to be a prime number, it would have been required that 399 has only two divisors, i.e., itself and 1.

Is 399 a deficient number?

Yes, 399 is a deficient number, that is to say 399 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 399 without 399 itself (that is 1 + 3 + 7 + 19 + 21 + 57 + 133 = 241).

Parity of 399

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

Find out more:

What is an even number?

Is 399 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 399 is about 19.975.

Thus, the square root of 399 is not an integer, and therefore 399 is not a square number.

What is the square number of 399?

The square of a number (here 399) is the result of the product of this number (399) by itself (i.e., 399 × 399); the square of 399 is sometimes called "raising 399 to the power 2", or "399 squared".

The square of 399 is 159 201 because 399 × 399 = 399² = 159 201.

As a consequence, 399 is the square root of 159 201.

Number of digits of 399

399 is a number with 3 digits.

What are the multiples of 399?

The multiples of 399 are all integers evenly divisible by 399, that is all numbers such that the remainder of the division by 399 is zero. There are infinitely many multiples of 399. The smallest multiples of 399 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 399 too, since 0 × 399 = 0
399: indeed, 399 is a multiple of itself, since 399 is evenly divisible by 399 (we have 399 / 399 = 1, so the remainder of this division is indeed zero)
798: indeed, 798 = 399 × 2
1 197: indeed, 1 197 = 399 × 3
1 596: indeed, 1 596 = 399 × 4
1 995: indeed, 1 995 = 399 × 5
etc.

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 399). 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 19.975). 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.

Numbers near 399

Preceding numbers: …397, 398
Following numbers: 400, 401…

Nearest numbers from 399

Preceding prime number: 397
Following prime number: 401