Prime Factorization is a mathematical function employed to segregate 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 finding the prime factors of a number, we can streamline fractions and equations, in addition learn the properties of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two major methods for performing prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. Both processes will grant you the same outcome.
Factor Tree Method
The first way is using a factor tree. To create a factor tree:
Initiate by writing the value you are attempting to factor at the start of the page.
Underneath, create branches for the factors.
Proceed by creating branches and factoring before you arrive at a prime number.
Here’s an instance of the thought 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.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this process, we can create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors in the end 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 begin utilizing a record of prime numbers. Note down the value you are trying to factor. Subsequently, divide the number by a prime number that divides evenly into it. It’s easiest 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 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 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
Although we’ve already worked by the means of a some examples, let’s do another one employing both methods.
Let’s use 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 clear.
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? No.
What is a prime number which 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has many realistic utilizations in mathematics. One of the primary applications is simplifying 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 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 clarified fraction of 1/3.
To see how this operates, let's utilize 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 cancel out any 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 remained with the streamlined fraction of 1/3.
Prime factorization additionally plays an important role in cryptography and computer science. As you proceed in sophisticated math and science studies, you will find further utilizations for prime factorization and be delighted you are a pro.
It’s Peak Hour to Enhance Your Math Skills
Prime factorization is an important concept in math which 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 skills.
If you need assistance conquering prime factorization, contemplate reaching out to Grade Potential tutoring for professional support. Grade Potential instructors are experienced and knowledgeable in mathematics. They can offer personalized learning and guidance to support you comprehend and utilize prime factorization in your studies.
With the help of Grade Potential tutoring, you could enhance your mathematical skills, boost your confidence, and attain your academic aims.
