Prime Factorization is a mathematical method used to break down a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can just be divided by 1 and themselves, for example 2, 3, 5, and 7.

By finding the prime factors of a number, we could streamline equations and fractions, in addition learn the characteristics of that number. Let’s take a closer look.

## Processes for Determining Prime Factorization

There are two main processes for performing prime factorization. You can use a factor tree, or you can factor by dividing by prime numbers. Both methods will yield you the exact outcome.

### Factor Tree Method

The first way is using a factor tree. To create a factor tree:

Start by noting the number you are attempting to factor at the start of the page.

Under it, make branches for the factors.

Continue creating branches and factoring until you attain a prime number.

Here’s an instance of the thought process:

We recognize that 6 * 6 = 36.

Is 6 a prime number? No. 2 * 3 = 6.

Are 2 and 3 prime numbers? Yes. We are done.

The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this procedure, we could create a factor tree for 36 as ensues.

As demonstrated, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.

### Division Method

The next process for finding the prime factorization of a number is to initiate utilizing a record of prime numbers. Write down the number you are attempting to factor. Then, divide the number by a prime number which divides evenly into it. It’s most convenient to initiate with the initial few prime numbers, like 2, 3, and 5.

Let’s utilize the division process for prime factorization of 36.

What is a prime number that divides into 36? 2 → 2 * 18 = 36

Is 18 a prime number? Nope.

What is a prime number which divides into 18? 2 → 2 * 9 = 18

Is 9 a prime number? No.

What is a prime number that divides into 9? 3 → 3 * 3 = 9

Is 3 a prime number? Yes. We are done here.

The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.

Using both process, we established the prime factorization for 36 is 2 * 2 * 3 * 3.

## Examples of Prime Factorization

Even though we’ve earlier worked through a some examples, let’s do another one utilizing both processes.

Let’s utilize a factor tree to work out the prime factorization of 100.

We learned that 4 * 25 = 100.

2 * 2 = 4, and 2 is a prime number. 5 * 5 = 25, and 5 is a prime number. We are done.

The prime factorization of 100 is 2 * 2 * 5 * 5.

Let’s test the division process:

What is the prime factorization for 100?

What is a prime number which divides into 100? 2 * 50 = 100

Is 50 a prime number? No.

What is a prime number which divides into 50? 2 * 25 = 50

Is 25 a prime number? No.

What is a prime number that divides into 25? 5 * 5 = 25

Is 5 a prime number? Yes. We are done.

The prime factorization of 100 is 2 * 2 * 5 * 5.

## Utilizations of Prime Factorization

Prime factorization has multiple real-life utilizations in math. One of the main uses is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and simplify the fraction.

For instance, the fraction 8/24 can be streamlined by solving the prime factorization of both numbers. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling out the common prime factor of 2, we are left with the streamlined fraction of 1/3.

To see how this operates, let's employ prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.

8 = 2 * 2 * 2

24 = 2 * 2 * 2 * 3

Subsequently, we cancel out any common prime factors among the numerator and denominator.

8/24 = 2 * 2 * 2 / 2 * 2 * 2 * 3 = 1/3

After canceling out the common prime factors of 2, we are left with the streamlined fraction of 1/3.

Prime factorization also plays an important role in computer science and cryptography. As you go ahead in advanced mathematics and science studies, you will figure out more utilizations for prime factorization and be delighted you are an expert.

## It’s Prime Time to Advance Your Math Abilities

Prime factorization is an important theory in math which enables us to simplify equations and fractions, as well as understand the properties of a number. By practicing and understanding the methods and applications of prime factorization, we could enhance our mathematical skills and analytical skills.

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