Is 330 a prime number?

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

For 330, the answer is: No, 330 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 330) is as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.

For 330 to be a prime number, it would have been required that 330 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 330 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 330 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

330 is a multiple of 1
330 is a multiple of 2
330 is a multiple of 3
330 is a multiple of 5
330 is a multiple of 6
330 is a multiple of 10
330 is a multiple of 11
330 is a multiple of 15
330 is a multiple of 22
330 is a multiple of 30
330 is a multiple of 33
330 is a multiple of 55
330 is a multiple of 66
330 is a multiple of 110
330 is a multiple of 165

For 330 to be a prime number, it would have been required that 330 has only two divisors, i.e., itself and 1.

Is 330 a deficient number?

No, 330 is not a deficient number: to be deficient, 330 should have been such that 330 is larger than the sum of its proper divisors, i.e., the divisors of 330 without 330 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 11 + 15 + 22 + 30 + 33 + 55 + 66 + 110 + 165 = 534).

In fact, 330 is an abundant number; 330 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 11 + 15 + 22 + 30 + 33 + 55 + 66 + 110 + 165 = 534). The smallest abundant number is 12.

Parity of 330

330 is an even number, because it is evenly divisible by 2: 330 / 2 = 165.

Find out more:

What is an even number?

Is 330 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 330 is about 18.166.

Thus, the square root of 330 is not an integer, and therefore 330 is not a square number.

What is the square number of 330?

The square of a number (here 330) is the result of the product of this number (330) by itself (i.e., 330 × 330); the square of 330 is sometimes called "raising 330 to the power 2", or "330 squared".

The square of 330 is 108 900 because 330 × 330 = 330² = 108 900.

As a consequence, 330 is the square root of 108 900.

Number of digits of 330

330 is a number with 3 digits.

What are the multiples of 330?

The multiples of 330 are all integers evenly divisible by 330, that is all numbers such that the remainder of the division by 330 is zero. There are infinitely many multiples of 330. The smallest multiples of 330 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 330 too, since 0 × 330 = 0
330: indeed, 330 is a multiple of itself, since 330 is evenly divisible by 330 (we have 330 / 330 = 1, so the remainder of this division is indeed zero)
660: indeed, 660 = 330 × 2
990: indeed, 990 = 330 × 3
1 320: indeed, 1 320 = 330 × 4
1 650: indeed, 1 650 = 330 × 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 330). 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 18.166). 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 330

Preceding numbers: …328, 329
Following numbers: 331, 332…

Nearest numbers from 330

Preceding prime number: 317
Following prime number: 331