Prime Factorization is a mathematical method used 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 just 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 understand the properties of that number. Let’s get a closer look.
Methods for Determining Prime Factorization
There are two primary methods for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. Both techniques will grant you the same answer.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Begin by noting the value you are trying to factor at the start of the page.
Under it, make branches for the factors.
Continue creating branches and factoring before you reach a prime number.
Here’s an example of the thought process:
We recognize that 6 * 6 = 36.
Is 6 a prime number? No. 2 * 3 = 6.
Are 2 and 3 prime numbers? Yes. We have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this process, we can make a factor tree for 36 as follows.
As you can see, 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 next method for working out the prime factorization of a number is to begin using a list of prime numbers. Note the value you are trying to factor. Subsequently, divide the value by a prime number which divides equally into it. It’s most convenient to begin 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 that 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 visualization.
Using both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked by the means of a few examples, let’s do another one utilizing both processes.
Let’s utilize a factor tree to figure out 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 done.
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 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 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.
Applications of Prime Factorization
Prime factorization has multiple real-life applications in math. One of the primary uses 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 could be streamlined by working out 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 clarified fraction of 1/3.
To check how this works, let's employ prime factorization to streamline the fraction 8/24. First, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out ever common prime factors within 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 further plays an essential role in cryptography and computer science. As you progress in advanced math and science studies, you will figure out more uses for prime factorization and be delighted you are a pro.
It’s the Best Time to Boost Your Mathematical Abilities
Prime factorization is a crucial theory in math that enables us to simplify equations and fractions, as well as learn the characteristics of a value. By practicing and comprehending the methods and uses of prime factorization, we could improve our mathematical skills and problem-solving abilities.
If you require help conquering prime factorization, contemplate reaching out to Grade Potential tutoring for professional assistance. Grade Potential tutors are experienced and knowledgeable in math. They could provide customized instruction and support to support you understand and utilize prime factorization in your studies.
With the assistance of Grade Potential tutoring, you can improve your mathematical skills, boost your confidence, and reach your academic goals.
