# Prime Factorization using Factor Trees

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

Example:

Find the prime factorization of 36.

Solution:

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

Review prime and composite numbers
A prime number natural number greater than 1 that only has two factors: one and itself.
Examples: 2,3,5,7,11,13,17,19, ...

A composite number is a natural number that has more than two factors.
The number 1 is neither prime nor composite.

Prime Factorization
To determine the prime factorization of a natural number, we need to find the prime numbers that when multiplied together gives us the original number.
We need to be careful not to confuse prime factorization with the factors of a number. The factors of a number are any two numbers whose product give the original number. Factors do not need to be prime.

We can find the prime factorization of a number using the factor tree.
Example:
Determine the prime factorization of the following numbers:
1. 24
2. 54
3. 120
4. 625
The following videos show more examples of finding prime factorization using factor trees.
Example:
Find the prime factorization of 12 Example:
Find the prime factorization of 72

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