Prime Factorization is a mathematical function utilized to break down 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 only be divided by 1 and themselves, for instance 2, 3, 5, and 7.

By figuring out the prime factors of a number, we could simplify fractions and equations, also understand the properties of that number. Let’s get a closer look.

## Processes for Finding Prime Factorization

There are two major methods for figuring out prime factorization. You could utilize a factor tree, or you could factor by dividing by prime numbers. Both techniques will give you the same answer.

### Factor Tree Method

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

Start by noting the value you are trying to factor at the start of the page.

Underneath, create branches for the factors.

Continue drawing branches and factoring till you reach 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 will be 2 x 2 x 3 x 3. To envision this procedure, we can create a factor tree for 36 as follows.

As demonstrated, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.

### Division Method

The second method for working out the prime factorization of a number is to start using a list of prime numbers. Note down the value you are attempting to factor. Then, divide the value by a prime number which divides evenly into it. It’s most convenient to start with the first 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? No.

What is a prime number that 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 chart.

Utilizing both systems, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.

## Examples of Prime Factorization

Even though we’ve earlier worked by the means of a few examples, let’s do one more employing both processes.

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

We know 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 here.

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 done.

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

## Uses of Prime Factorization

Prime factorization has many realistic uses in mathematics. One of the primary uses is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline the fraction.

For instance, the fraction 8/24 could 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 check how this works, let's employ prime factorization to simplify the fraction 8/24. Primarily, work on prime factorization of the numerator and denominator.

8 = 2 * 2 * 2

24 = 2 * 2 * 2 * 3

Then, we rule out ever common prime factors between 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 further plays an essential part in cryptography and computer science. As you proceed in progressive mathematics and science theories, you will find more applications for prime factorization and be glad you are a pro.

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

Prime factorization is an important concept in mathematics that enables us to simplify equations and fractions, also get a grasp of the properties of a number. By practicing and understanding the methods and uses of prime factorization, we can improve our math abilities and analytical abilities.

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