Is 33 a prime number? What are the divisors of 33?

Is 33 a prime number?

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

For 33, the answer is: No, 33 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 33) is as follows: 1, 3, 11, 33.

To be 33 a prime number, it would have been required that 33 has only two divisors, i.e., itself and 1.

As a consequence:

  • 33 is a multiple of 1
  • 33 is a multiple of 3
  • 33 is a multiple of 11

To be 33 a prime number, it would have been required that 33 has only two divisors, i.e., itself and 1.

However, 33 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 33 = 3 x 11, where 3 and 11 are both prime numbers.

Is 33 a deficient number?

Yes, 33 is a deficient number, that is to say 33 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 33 without 33 itself (that is 1 + 3 + 11 = 15).

Parity of 33

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

Is 33 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 33 is about 5.745.

Thus, the square root of 33 is not an integer, and therefore 33 is not a square number.

What is the square number of 33?

The square of a number (here 33) is the result of the product of this number (33) by itself (i.e., 33 × 33); the square of 33 is sometimes called "raising 33 to the power 2", or "33 squared".

The square of 33 is 1 089 because 33 × 33 = 332 = 1 089.

As a consequence, 33 is the square root of 1 089.

Number of digits of 33

33 is a number with 2 digits.

What are the multiples of 33?

The multiples of 33 are all integers evenly divisible by 33, that is all numbers such that the remainder of the division by 33 is zero. There are infinitely many multiples of 33. The smallest multiples of 33 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 33 too, since 0 × 33 = 0
  • 33: indeed, 33 is a multiple of itself, since 33 is evenly divisible by 33 (we have 33 / 33 = 1, so the remainder of this division is indeed zero)
  • 66: indeed, 66 = 33 × 2
  • 99: indeed, 99 = 33 × 3
  • 132: indeed, 132 = 33 × 4
  • 165: indeed, 165 = 33 × 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 33). 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 5.745). 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 33

  • Preceding numbers: …31, 32
  • Following numbers: 34, 35

Nearest numbers from 33

  • Preceding prime number: 31
  • Following prime number: 37
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