Prime Factorization is a mathematical method employed 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 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, in addition learn the properties of that number. Let’s take a closer look.
Methods for Figuring out Prime Factorization
There are two primary methods for working out prime factorization. You could use a factor tree, or you can factor by dividing by prime numbers. Both methods will give you the exact outcome.
Factor Tree Method
The primary method is utilizing a factor tree. To create a factor tree:
Begin by writing the value you are trying to factor at the top of the page.
Under it, create branches for the factors.
Continue creating branches and factoring before you arrive at a prime number.
Here’s an instance 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this method, we could make a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second process for working out the prime factorization of a number is to start utilizing a record of prime numbers. Note down the number you are trying to factor. Subsequently, divide the value by a prime number that divides evenly into it. It’s simplest to begin with the initial 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 that divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
What is a prime number that 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 depiction.
Utilizing both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked by the means of a some examples, let’s do another one employing both methods.
Let’s use 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 here.
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 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 done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has multiple practical applications in math. One of the main applications is streamlining fractions. By finding out 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 could be simplified by working out 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 simplified fraction of 1/3.
To check how this functions, let's utilize 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
Next, we cancel out ever common prime factors within 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 left with the streamlined fraction of 1/3.
Prime factorization additionally executes a crucial role in cryptography and computer science. As you go ahead in advanced math and science theories, you will find additional uses for prime factorization and be glad you are a professional.
It’s Peak Hour to Advance Your Mathematical Abilities
Prime factorization is an important concept in mathematics that enables us to simplify equations and fractions, moreover understand the characteristics of a number. By practicing and comprehending the processes and applications of prime factorization, we could enhance our mathematical abilities and analytical abilities.
If you require help conquering prime factorization, consider connect with Grade Potential tutoring for professional assistance. Grade Potential tutors are experienced and educated in mathematics. They could offer personalized instruction and assistance to support you learn and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can enhance your mathematical abilities, improve your confidence, and achieve your academic aims.
