Is 393 a prime number?

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

For 393, the answer is: No, 393 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 393) is as follows: 1, 3, 131, 393.

For 393 to be a prime number, it would have been required that 393 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

393 is a multiple of 1
393 is a multiple of 3
393 is a multiple of 131

For 393 to be a prime number, it would have been required that 393 has only two divisors, i.e., itself and 1.

However, 393 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 393 = 3 x 131, where 3 and 131 are both prime numbers.

Is 393 a deficient number?

Yes, 393 is a deficient number, that is to say 393 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 393 without 393 itself (that is 1 + 3 + 131 = 135).

Parity of 393

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

Find out more:

What is an even number?

Is 393 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 393 is about 19.824.

Thus, the square root of 393 is not an integer, and therefore 393 is not a square number.

What is the square number of 393?

The square of a number (here 393) is the result of the product of this number (393) by itself (i.e., 393 × 393); the square of 393 is sometimes called "raising 393 to the power 2", or "393 squared".

The square of 393 is 154 449 because 393 × 393 = 393² = 154 449.

As a consequence, 393 is the square root of 154 449.

Number of digits of 393

393 is a number with 3 digits.

What are the multiples of 393?

The multiples of 393 are all integers evenly divisible by 393, that is all numbers such that the remainder of the division by 393 is zero. There are infinitely many multiples of 393. The smallest multiples of 393 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 393 too, since 0 × 393 = 0
393: indeed, 393 is a multiple of itself, since 393 is evenly divisible by 393 (we have 393 / 393 = 1, so the remainder of this division is indeed zero)
786: indeed, 786 = 393 × 2
1 179: indeed, 1 179 = 393 × 3
1 572: indeed, 1 572 = 393 × 4
1 965: indeed, 1 965 = 393 × 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 393). 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 19.824). 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 393

Preceding numbers: …391, 392
Following numbers: 394, 395…

Nearest numbers from 393

Preceding prime number: 389
Following prime number: 397