Is 333 a prime number?

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

For 333, the answer is: No, 333 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 333) is as follows: 1, 3, 9, 37, 111, 333.

For 333 to be a prime number, it would have been required that 333 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

333 is a multiple of 1
333 is a multiple of 3
333 is a multiple of 9
333 is a multiple of 37
333 is a multiple of 111

For 333 to be a prime number, it would have been required that 333 has only two divisors, i.e., itself and 1.

Is 333 a deficient number?

Yes, 333 is a deficient number, that is to say 333 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 333 without 333 itself (that is 1 + 3 + 9 + 37 + 111 = 161).

Parity of 333

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

Find out more:

What is an even number?

Is 333 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 333 is about 18.248.

Thus, the square root of 333 is not an integer, and therefore 333 is not a square number.

What is the square number of 333?

The square of a number (here 333) is the result of the product of this number (333) by itself (i.e., 333 × 333); the square of 333 is sometimes called "raising 333 to the power 2", or "333 squared".

The square of 333 is 110 889 because 333 × 333 = 333² = 110 889.

As a consequence, 333 is the square root of 110 889.

Number of digits of 333

333 is a number with 3 digits.

What are the multiples of 333?

The multiples of 333 are all integers evenly divisible by 333, that is all numbers such that the remainder of the division by 333 is zero. There are infinitely many multiples of 333. The smallest multiples of 333 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 333 too, since 0 × 333 = 0
333: indeed, 333 is a multiple of itself, since 333 is evenly divisible by 333 (we have 333 / 333 = 1, so the remainder of this division is indeed zero)
666: indeed, 666 = 333 × 2
999: indeed, 999 = 333 × 3
1 332: indeed, 1 332 = 333 × 4
1 665: indeed, 1 665 = 333 × 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 333). 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 18.248). 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 333

Preceding numbers: …331, 332
Following numbers: 334, 335…

Nearest numbers from 333

Preceding prime number: 331
Following prime number: 337