Is 398 a prime number?

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

For 398, the answer is: No, 398 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 398) is as follows: 1, 2, 199, 398.

For 398 to be a prime number, it would have been required that 398 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

398 is a multiple of 1
398 is a multiple of 2
398 is a multiple of 199

For 398 to be a prime number, it would have been required that 398 has only two divisors, i.e., itself and 1.

However, 398 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 398 = 2 x 199, where 2 and 199 are both prime numbers.

Is 398 a deficient number?

Yes, 398 is a deficient number, that is to say 398 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 398 without 398 itself (that is 1 + 2 + 199 = 202).

Parity of 398

398 is an even number, because it is evenly divisible by 2: 398 / 2 = 199.

Find out more:

What is an even number?

Is 398 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 398 is about 19.950.

Thus, the square root of 398 is not an integer, and therefore 398 is not a square number.

What is the square number of 398?

The square of a number (here 398) is the result of the product of this number (398) by itself (i.e., 398 × 398); the square of 398 is sometimes called "raising 398 to the power 2", or "398 squared".

The square of 398 is 158 404 because 398 × 398 = 398² = 158 404.

As a consequence, 398 is the square root of 158 404.

Number of digits of 398

398 is a number with 3 digits.

What are the multiples of 398?

The multiples of 398 are all integers evenly divisible by 398, that is all numbers such that the remainder of the division by 398 is zero. There are infinitely many multiples of 398. The smallest multiples of 398 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 398 too, since 0 × 398 = 0
398: indeed, 398 is a multiple of itself, since 398 is evenly divisible by 398 (we have 398 / 398 = 1, so the remainder of this division is indeed zero)
796: indeed, 796 = 398 × 2
1 194: indeed, 1 194 = 398 × 3
1 592: indeed, 1 592 = 398 × 4
1 990: indeed, 1 990 = 398 × 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 398). 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 19.950). 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 398

Preceding numbers: …396, 397
Following numbers: 399, 400…

Nearest numbers from 398

Preceding prime number: 397
Following prime number: 401