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Prime Factorization

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More Lessons for Arithmetic

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Every composite number can be expressed as a product of prime factors. We can use a factor tree to find the prime factors.


Find the prime factors of 36.


The prime factors of 36 are 2 and 3.

We can write 36 as a product of prime factors: 2 × 2 × 3 × 3

The factor tree method is quite flexible – at each branch you can break the number into any factors until you reach the prime factors.

The result is the same: 36 = 3 × 2 × 2 × 3

Although the order of the factors may be different because we can start with different pairs of factors, every factor tree of 36 has the same prime factorization.

We can also use exponents to write the prime factorization.

36 = 2 2 × 3 2

The following videos show more prime factorization examples using the factor tree.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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