# Factors and Prime Factorization

Mathematics is all about numbers and the study of their types, properties, and concepts. Arithmetic is the branch of mathematics that is a study of numbers and their properties. It includes the operations and manipulation of numbers. Factors are key concepts taught in arithmetic at the elementary stage. A factor is a number that gives no remainder after it is divided by a specific number. Factors of a number are terminable.

Factoring is a valuable skill utilized in real-life situations, such as dividing something into equal parts or dividing into rows and columns, comparing prices, exchanging money and understanding time, and making calculations during travel.

## What are Factors?

The term ‘factors’ is derived from a Latin word that means a maker. A factor represents the numbers that divide the given number absolutely, without leaving any remainder. For example, 4 is the factor of 12 since on dividing 12 by 4, we get 3, and it does not leave any remainder. The other factors of 12 are 1, 2, 3, and 6. Moreover, factors are the numbers one can multiply with each other to obtain the required number. Every number has a minimum of two factors, i.e., one and the number itself. A number that has only two factors is known as Prime Numbers.

To determine the factors of a given number, you need to identify the numbers that evenly divide that particular number. In order to do so, start with dividing by number one, as one is the factor of every number. Almost every number can be represented as the product of its prime factors. This process is called the prime factorization of a number.

## What is Prime Factorization?

Prime factorization is a process of representing a number as a product of its prime numbers. It is also known as integer factorization or prime decomposition. This method helps find out which prime numbers multiply together to form a number & it is also useful in finding the factors of composite numbers, LCM & HCF of any given set of numbers.

One of the major applications of prime factorization is cryptography. Cryptography is a practice of protecting digital information and communicating it through the use of codes. It is a useful technique practiced by computer programmers to build a unique code with numbers. Such kind of encoded information is quite convenient for computers to process and transfer securely.

## Simple & Easy Methods to Learn Prime Factorization:

Learning prime factorization of a large number is presumed an important skill that appears little complex to attain for some children. Solving such complex problems requires a thorough step-by-step understanding of the factorization process. There are two main prime factorization methods through which we can quickly learn to find the factors of a number:

- Division Method.
- Fraction Tree Method.

### Prime Factorization by Division Method:

The division method is one of the simplest ways to get the prime factors. Using the division method, you can easily find the prime factor by dividing the given number by the smallest prime number. Here are the steps to learn prime factorization through the division method:

- Divide the given number by the smallest prime number that divides the number exactly.
- Proceed again by dividing the quotient with the smallest prime number and repeat it until the quotient is 1.
- Once the quotient becomes 1, multiply all the factors to get the prime factor of the number.

### Prime factorization by Factor Tree Method:

One of the most common methods for learning prime decomposition involves the formation of factor trees. Factor trees enable students to visualize the multiplicative breakdown of a number. It also helps them to develop a conceptual understanding of prime factorization. Here are the steps to learn prime factorization through the factor tree method

- Write the given on the top to use it as the root of the factor tree.
- Break down the number in the pair of its factors and consider them as the tree’s next branches.
- Repeatedly factorize the composite factors to put down the factor pairs further as the branches.
- Continue the process until you get the prime factors of all the composite factors.