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# Explain prime factorization of numbers using factor trees with example.

__Solution:__

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**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 48.

Solution:

48

/ \

4 12

/ \ / \

2 2 2 6

/ \

2 3

We continue breaking the numbers till prime factors are reached. We are using here factor trees to find the prime factorization of a number; here it is 48.

The prime factors of 36 are 2 and 3.

We can write 48 as a product of prime factors: 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 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: 48 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3

Although the order of the factors may be different because we can start with different pairs of factors, every factor tree of 48 has the same prime factorization.

We can also use exponents to write the prime factorization.

$48 = 2^4 \times 3$

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