Prime Factorization is a mathematical function utilized to split up a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can just be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we can streamline fractions and equations, also learn the characteristics of that number. Let’s take a closer look.
Processes for Figuring out Prime Factorization
There are two main methods for performing prime factorization. You could employ a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will grant you the exact outcome.
Factor Tree Method
The initial method is utilizing a factor tree. To make a factor tree:
Start by writing the number you are attempting to factor at the top of the page.
Under it, create branches for the factors.
Proceed by making branches and factoring till you attain a prime number.
Here’s an example of the thought process:
We know 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 visualize this process, we can create a factor tree for 36 as ensues.
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 process for figuring out the prime factorization of a number is to begin using a list of prime numbers. Write down the value you are trying to factor. Then, divide the value by a prime number which divides evenly into it. It’s simplest to begin 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? 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 which 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 found 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 some examples, let’s do another one utilizing both processes.
Let’s utilize a factor tree to find 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 clear.
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? Nope.
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.
Utilizations of Prime Factorization
Prime factorization has many realistic utilizations in math. One of the main applications is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For example, the fraction 8/24 can be simplified by solving 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 streamlined fraction of 1/3.
To check how this functions, let's employ prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we rule out ever common prime factors among 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 additionally executes an essential role in cryptography and computer science. As you proceed in advanced math and science concepts, you will find further uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Boost Your Math Skills
Prime factorization is an essential concept in mathematics which allows us to streamline equations and fractions, as well as understand the characteristics of a value. By practicing and comprehending the processes and utilizations of prime factorization, we could enhance our math skills and analytical skills.
If you need support conquering prime factorization, consider contacting with Grade Potential tutoring for expert support. Grade Potential tutors are skilled and knowledgeable in math. They can offer personalized learning and support to support you comprehend and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you could advance your math skills, boost your confidence, and attain your academic objectives.
