Prime Factorization is a mathematical function employed to split up a composite number into its prime factors. Composite numbers can be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can only be divided by 1 and themselves, for instance 2, 3, 5, and 7.

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

## Methods for Determining Prime Factorization

There are two primary methods for figuring out prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both methods will give you the exact outcome.

### Factor Tree Method

The primary way is utilizing a factor tree. To create a factor tree:

Initiate by noting the value you are attempting to factor at the start of the page.

Under it, make branches for the factors.

Proceed by drawing branches and factoring till you arrive at a prime number.

Here’s an example 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 have reached the end.

The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this method, we can create a factor tree for 36 as follows.

As you can see, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.

### Division Method

The next process for working out the prime factorization of a number is to begin using a list of prime numbers. Note down the number you are trying to factor. Subsequently, divide the number by a prime number which divides equally into it. It’s most convenient to start with the initial few prime numbers, like 2, 3, and 5.

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

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

Is 18 a prime number? Nope.

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

Is 9 a prime number? Nope.

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

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

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

Utilizing both methods, we established the prime factorization for 36 is 2 * 2 * 3 * 3.

## Examples of Prime Factorization

Even though we’ve previously worked through a some examples, let’s do one more employing both processes.

Let’s utilize a factor tree to figure 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 try 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? Nope.

What is a prime number that 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 clear.

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

## Applications of Prime Factorization

Prime factorization has many real-life uses in mathematics. One of the major uses is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.

For example, the fraction 8/24 could be streamlined by finding the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By ruling out the common prime factor of 2, we are left with the clarified fraction of 1/3.

To check how this works, let's use prime factorization to simplify the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.

8 = 2 * 2 * 2

24 = 2 * 2 * 2 * 3

Next, we rule out any common prime factors among the numerator and denominator.

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

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

Prime factorization also plays an essential part in computer science and cryptography. As you proceed in progressive mathematics and science studies, you will figure out further utilizations for prime factorization and be pleased you are an expert.

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

Prime factorization is a crucial concept in mathematics which enables us to simplify equations and fractions, also get a grasp of the characteristics of a value. By practicing and comprehending the methods and utilizations of prime factorization, we can improve our math abilities and analytical skills.

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