Prime Factorization is a mathematical method used to break down 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 can simplify fractions and equations, in addition understand the characteristics of that number. Let’s look closely.
Ways for Determining Prime Factorization
There are two major ways for performing prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will yield you the same answer.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Start by noting the number you are trying to factor at the start of the page.
Under it, create branches for the factors.
Continue making branches and factoring till you reach a prime number.
Here’s an example of the thinking 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 will be 2 x 2 x 3 x 3. To envision this method, we can create a factor tree for 36 as ensues.
Consequently, 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 second way for figuring out the prime factorization of a number is to initiate using a list of prime numbers. Write down the value you are trying to factor. Next, 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 use 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? No.
What is a prime number that divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? No.
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 visualization.
Using both systems, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve already worked by the means of a few examples, let’s do another one employing both methods.
Let’s utilize a factor tree to figure out 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.
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? No.
What is a prime number which 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.
Uses of Prime Factorization
Prime factorization has multiple real-life applications in mathematics. One of the main applications is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 can be streamlined by finding the prime factorization of both numbers. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By ruling out the common prime factor of 2, we are left with the streamlined fraction of 1/3.
To see how this works, let's use prime factorization to streamline the fraction 8/24. Foremost, 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 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 additionally plays a crucial role in computer science and cryptography. As you progress in sophisticated math and science theories, you will find more utilizations for prime factorization and be glad you are a professional.
It’s Prime Time to Enhance Your Mathematical Abilities
Prime factorization is an important concept in math that enables us to simplify equations and fractions, as well as understand the characteristics of a number. By practicing and understanding the methods and applications of prime factorization, we could improve our math abilities and problem-solving abilities.
If you require help conquering prime factorization, consider reaching out to Grade Potential tutoring for professional support. Grade Potential teachers are skilled and educated in mathematics. They can provide personalized learning and guidance to support you understand and apply prime factorization in your studies.
With the support of Grade Potential tutoring, you can enhance your mathematical skills, improve your confidence, and reach your academic objectives.
