Is 329 a prime number?

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

For 329, the answer is: No, 329 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 329) is as follows: 1, 7, 47, 329.

For 329 to be a prime number, it would have been required that 329 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

329 is a multiple of 1
329 is a multiple of 7
329 is a multiple of 47

For 329 to be a prime number, it would have been required that 329 has only two divisors, i.e., itself and 1.

However, 329 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 329 = 7 x 47, where 7 and 47 are both prime numbers.

Is 329 a deficient number?

Yes, 329 is a deficient number, that is to say 329 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 329 without 329 itself (that is 1 + 7 + 47 = 55).

Parity of 329

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

Find out more:

What is an even number?

Is 329 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 329 is about 18.138.

Thus, the square root of 329 is not an integer, and therefore 329 is not a square number.

What is the square number of 329?

The square of a number (here 329) is the result of the product of this number (329) by itself (i.e., 329 × 329); the square of 329 is sometimes called "raising 329 to the power 2", or "329 squared".

The square of 329 is 108 241 because 329 × 329 = 329² = 108 241.

As a consequence, 329 is the square root of 108 241.

Number of digits of 329

329 is a number with 3 digits.

What are the multiples of 329?

The multiples of 329 are all integers evenly divisible by 329, that is all numbers such that the remainder of the division by 329 is zero. There are infinitely many multiples of 329. The smallest multiples of 329 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 329 too, since 0 × 329 = 0
329: indeed, 329 is a multiple of itself, since 329 is evenly divisible by 329 (we have 329 / 329 = 1, so the remainder of this division is indeed zero)
658: indeed, 658 = 329 × 2
987: indeed, 987 = 329 × 3
1 316: indeed, 1 316 = 329 × 4
1 645: indeed, 1 645 = 329 × 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 329). 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 18.138). 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 329

Preceding numbers: …327, 328
Following numbers: 330, 331…

Nearest numbers from 329

Preceding prime number: 317
Following prime number: 331