# What is Prime Factorization Mean in Math?

Prime factorization is a method of expressing a number as a product of its prime **factors**. A number that has exactly two factors, 1, and the number itself is a **prime number**. For example, if we consider the number 42. We know that 42 = 6 Ã— 7, but 6 is not a prime number. The number 6 can be factorized as 2Ã— 3, where 2 and 3 are prime numbers.

The prime factorization of number 42 = 2Ã— 3 Ã— 7, where all the factors are prime numbers.

In this article learn more about prime factorization with different mathematical problems followed by solved examples.

**What is the Prime Factorization?**

The way of writing a number as the product of prime numbers is said to be prime factorization. In other words, the process of breaking down a number into its prime numbers that help in forming the number when multiplied is called prime factorization. The numbers have only two factors, 1, and the number itself is called a prime number. Let 2, 3, 5, 7, 11, 13, 17, 19, and so on are examples of prime numbers. Prime factorization of any number means to indicate that number as a product of prime numbers.

** For example,** the prime factorization of 30 can be done in the following way

**What are Prime Factors and Factors?**

Factors of a number are the numbers that are multiplied to obtain the original number. For example, 6 and 5 are the factors of 30, i.e., 5 Ã— 6 = 30, whereas, prime factors of a number are the prime numbers that are multiplied to obtain the original number. For example: 2, 3, and 5 are the prime factors of 30, i.e., 2 Ã— 3Ã— 5 = 30.

**Method of Prime factorization**

There are different ways for the prime factorization of a number. Used for prime factorization the most common methods are given below:

- Prime factorization by factor tree method
- Prime factorization by division method

**Prime Factorization of a Number**

See the prime factorization for a few numbers

Number | Prime factorization |

24 | 2^{3} Ã— 3 |

72 | 2^{3} Ã— 3^{2} |

48 | 2^{4} Ã— 3 |

36 | 2^{2 }Ã— 3^{2} |

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