Prime Factorization is a mathematical method employed to split up a composite number into its prime factors. Composite numbers can 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, such as 2, 3, 5, and 7.

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

## Ways for Finding Prime Factorization

There are two primary ways 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 first method is utilizing a factor tree. To create a factor tree:

Begin by noting the value you are trying to factor at the top of the page.

Under it, make branches for the factors.

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

Here’s an instance 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 will be 2 x 2 x 3 x 3. To imagine this process, we could make a factor tree for 36 as ensues.

As you can see, 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 method for figuring out the prime factorization of a number is to begin using a record of prime numbers. Note down the value you are trying to factor. Then, divide the value by a prime number that divides equally into it. It’s simplest to initiate with the initial few prime numbers, like 2, 3, and 5.

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

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

Is 18 a prime number? No.

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.

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

## Examples of Prime Factorization

Although we’ve earlier worked by the means of a few examples, let’s do one more utilizing both methods.

Let’s use 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 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? Nope.

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

Is 25 a prime number? Nope.

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.

## Uses of Prime Factorization

Prime factorization has multiple real-life applications in math. One of the primary uses is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.

For example, the fraction 8/24 can be simplified 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 utilize prime factorization to simplify the fraction 8/24. First, work on prime factorization of the numerator and denominator.

8 = 2 * 2 * 2

24 = 2 * 2 * 2 * 3

Then, we cancel out ever common prime factors between 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 simplified fraction of 1/3.

Prime factorization additionally plays an essential role in computer science and cryptography. As you proceed in advanced mathematics and science theories, you will find additional applications for prime factorization and be delighted you are an expert.

## It’s Peak Hour to Advance Your Math Abilities

Prime factorization is an essential concept in mathematics that allows us to streamline equations and fractions, also learn the characteristics of a value. By practicing and comprehending the methods and uses of prime factorization, we can improve our mathematical abilities and analytical skills.

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