Prime Factorization is a mathematical method utilized to split up 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 only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could streamline fractions and equations, as well as learn the properties of that number. Let’s look closely.
Ways for Figuring out Prime Factorization
There are two primary processes for working out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other processes will grant you the same answer.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Begin by writing the number you are attempting to factor at the start of the page.
Under it, create branches for the factors.
Continue drawing branches and factoring before you attain a prime number.
Here’s an example of the thinking 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 would be 2 x 2 x 3 x 3. To imagine this method, we could make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second way for working out the prime factorization of a number is to initiate using a list of prime numbers. Write down the value you are attempting to factor. Subsequently, divide the number by a prime number that divides evenly into it. It’s simplest to initiate with the initial few prime numbers, like 2, 3, and 5.
Let’s utilize the division process 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 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.
Utilizing both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked through a few examples, let’s do one more utilizing both methods.
Let’s use a factor tree to work 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 clear.
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 that 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? Nope.
What is a prime number which 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 mathematics. One of the major utilizations is streamlining fractions. By finding 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 could 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 clarified fraction of 1/3.
To see how this functions, let's utilize prime factorization to streamline the fraction 8/24. Primarily, perform 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 also executes an important part in cryptography and computer science. As you go ahead in sophisticated mathematics and science theories, you will find further applications for prime factorization and be glad you are a pro.
It’s Peak Hour to Boost Your Mathematical Skills
Prime factorization is an important theory in math which enables us to simplify equations and fractions, as well as learn the characteristics of a number. By practicing and comprehending the methods and utilizations of prime factorization, we could improve our math skills and analytical skills.
If you require assistance mastering prime factorization, contemplate connect with Grade Potential tutoring for professional support. Grade Potential instructors are experienced and educated in mathematics. They could offer customized instruction and support to support you comprehend and utilize prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could improve your mathematical abilities, improve your confidence, and reach your academic aims.
