Is 321 a prime number?

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

For 321, the answer is: No, 321 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 321) is as follows: 1, 3, 107, 321.

For 321 to be a prime number, it would have been required that 321 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

321 is a multiple of 1
321 is a multiple of 3
321 is a multiple of 107

For 321 to be a prime number, it would have been required that 321 has only two divisors, i.e., itself and 1.

However, 321 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 321 = 3 x 107, where 3 and 107 are both prime numbers.

Is 321 a deficient number?

Yes, 321 is a deficient number, that is to say 321 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 321 without 321 itself (that is 1 + 3 + 107 = 111).

Parity of 321

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

Find out more:

What is an even number?

Is 321 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 321 is about 17.916.

Thus, the square root of 321 is not an integer, and therefore 321 is not a square number.

What is the square number of 321?

The square of a number (here 321) is the result of the product of this number (321) by itself (i.e., 321 × 321); the square of 321 is sometimes called "raising 321 to the power 2", or "321 squared".

The square of 321 is 103 041 because 321 × 321 = 321² = 103 041.

As a consequence, 321 is the square root of 103 041.

Number of digits of 321

321 is a number with 3 digits.

What are the multiples of 321?

The multiples of 321 are all integers evenly divisible by 321, that is all numbers such that the remainder of the division by 321 is zero. There are infinitely many multiples of 321. The smallest multiples of 321 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 321 too, since 0 × 321 = 0
321: indeed, 321 is a multiple of itself, since 321 is evenly divisible by 321 (we have 321 / 321 = 1, so the remainder of this division is indeed zero)
642: indeed, 642 = 321 × 2
963: indeed, 963 = 321 × 3
1 284: indeed, 1 284 = 321 × 4
1 605: indeed, 1 605 = 321 × 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 321). 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 17.916). 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 321

Preceding numbers: …319, 320
Following numbers: 322, 323…

Nearest numbers from 321

Preceding prime number: 317
Following prime number: 331