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

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

## Methods for Determining Prime Factorization

There are two major ways for working out prime factorization. You can use a factor tree, or you can factor by dividing by prime numbers. One as well as the other processes will grant you the exact result.

### Factor Tree Method

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

Initiate by noting the number you are trying to factor at the top of the page.

Underneath, make branches for the factors.

Proceed by creating branches and factoring before you attain a prime number.

Here’s an example of the thinking process:

We understand that 6 * 6 = 36.

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

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

The prime factorization of 36 would be 2 x 2 x 3 x 3. To envision this procedure, we could make a factor tree for 36 as follows.

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

### Division Method

The second method for finding the prime factorization of a number is to initiate utilizing a list of prime numbers. Note the number you are attempting to factor. Then, divide the value by a prime number which divides evenly into it. It’s most convenient to initiate with the first 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 that 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 visualization.

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

## Examples of Prime Factorization

Even though we’ve previously worked by the means of a some examples, let’s do another one utilizing both processes.

Let’s use 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 try the division method:

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 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 done here.

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

## Utilizations of Prime Factorization

Prime factorization has several practical applications in math. One of the major uses is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and simplify the fraction.

For example, the fraction 8/24 could be streamlined by finding 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 use prime factorization to simplify the fraction 8/24. Foremost, 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 within 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 simplified fraction of 1/3.

Prime factorization further plays an important part in computer science and cryptography. As you progress in progressive math and science concepts, you will find more utilizations for prime factorization and be delighted you are a pro.

## It’s the Best Time to Advance Your Mathematical Abilities

Prime factorization is an important theory in math that enables us to streamline equations and fractions, moreover learn the characteristics of a value. By practicing and comprehending the processes and applications of prime factorization, we could improve our mathematical abilities and analytical skills.

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