Factors of 33
2026-02-28 10:34 Diff
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Last updated on December 11, 2025

The factors of 33 are natural numbers that divide 33 without leaving any remainder, or in other words, the factors of 33 divide 33 evenly. The multiple factors of 36 provide varieties of options for organising the space efficiently, especially in the classroom.

What are the factors of 33

The factors of 33 are 1, 3, 11, and 33.

Negative Factors- These are negative counterparts of the positive factors.


Negative factors are -1, -3, -11, -13.

Prime Factors- Prime factors are the prime numbers when multiplied together, giving 33 as the product.


Prime factors are 3 and 11.

Prime Factorization- The prime factorization of 33 = 3 ×11. This says 33 can be expressed as the product of the prime numbers 3 and 11.

The sum of Factors 33- The factors of 33 are 1, 3, 11, and 33. 


The sum of the factors of 33 = 1 + 3 + 11 + 33 = 48.

How to find the Factors of 33.

The systematic way to solve this problem is

Step 1: Start with the number one, every number has divisible by one√.
Step 2: Check numbers from 2 to the square root of 33, √33 is 5.74, now you need to check only numbers from 2 to 5.
Step 3: If a number divides 33 evenly, its pair is also a factor.

Now, let us implement to 33

  • 2 is not factor of 33
  • 3 is a factor of 33
  • 4 is not a factor of 33
  • 5 is not a factor of 33

Hence, derived from the above calculation are 1, 3, 11, and 33.
 

Finding Factors Using Multiplication

To find the factors of 33 using multiplication, we need to consider pairs of numbers that multiply together to equal 33.

While the square root of 33 = 5.74, we need to check until 5. Let us check the divisibility till 5.

  • 1 times 33 equals 33.
  • 2 can not divide 33 evenly.
  • 3 times 11 equals 33.
  • 4 can not divide 33 evenly.
  • 5 can not divide 33 evenly.

Therefore, the factors of 33 = 1, 3, 11, and 33.
 

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Finding Factors by Division Method

The division method involves systematically dividing 33 by all numbers from 1 to the square root of 33. If the answer is in whole number, then number and quotient are factors of 33.

  • 33 ÷ 1 = 33 (Both 1 and 33 are factors)
  • 33 ÷ 2 = 16.5 (Not a whole number, it is not a factor)
  • 33 ÷ 3 = 11 (Both 3 and 11 are factors)
  • 33 ÷ 4 = 8.25 (Not a whole number, it is not a factor)
  • 33 ÷ 5 = 6.6 (Not a whole number, it is not a factor)

Then, the factors of 33 will be 1, 3, 11, and 33.
 

Prime Factors and Prime Factorization

Prime Factors of 33- The prime factors of 33 are the prime numbers that divide 33 evenly.

  Prime Factorization of 33- The prime factorization of 33 is the expression of 33 as a product of its prime factors.


For 33, the prime factorization is 3×11.

This means that 33 is specially expressed as the product of the prime numbers 3 and 11.
 

Factor tree

A factor tree is a visual representation of the prime factorization of a number.<image>


Hence, 33 can be split into the prime factors 3 and 11.

Factor Pairs: A factor pair is said to be two numbers that multiply together to give a specific product. For 33, the factor pairs are:

1 and 33: 1×33 =33


3 and 11: 3×11 =33

33 is a relatively small number with few divisors.


Positive Pair Factors = 1and 33


Negative Pair Factors = -1 and -33

Common Mistakes and How to Avoid Them in Factors of 33

some common mistakes with their solutions are given below:

FAQs on Factors of 33

1.Does 33 have four factors?

Yes, factors of 33 is 1, 3, 11 and 33.

2.What is the GCF of 33?

Factor of 33 is 1 and 33. Therefore, the GCF of 33 is 33 itself.
 

3.Is 33 a factor of 6?

33 is not greater than 6, so it cannot be a factor of 6. The factor of 6 are 1, 2, 3, and 6.

4.Is 33 a factor of 9?

33 is greater than 9, it cannot be a factor of 9. The factor of 9 are 1, 3, and 9.

Important Glossaries for Factors of 33

  • Quotient: It is the number that gets as a result of division
  • Factors: Numbers that divide the given number completely without any remainder.
  • Prime Factors: Prime numbers that multiply together to form the given number.
  • Prime Factorization: Process of breaking down the number into prime factors

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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: She loves to read number jokes and games.