Prime Factorization is a mathematical function utilized 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 could streamline fractions and equations, as well as understand the properties of that number. Let’s get a closer look.
Ways for Figuring out Prime Factorization
There are two main methods for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. Both methods will grant you the same outcome.
Factor Tree Method
The initial way is using a factor tree. To create a factor tree:
Begin by noting the number you are trying to factor at the top of the page.
Underneath, make branches for the factors.
Continue making branches and factoring until you reach 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 imagine this method, we can create a factor tree for 36 as follows.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next method for figuring out the prime factorization of a number is to start utilizing a list of prime numbers. Note down the value you are trying to factor. Next, divide the value by a prime number which divides evenly into it. It’s most convenient to start with the first 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? Nope.
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 systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked by the means of a few examples, let’s do one more employing both methods.
Let’s utilize 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 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.
Applications of Prime Factorization
Prime factorization has several real-life applications in mathematics. One of the main utilizations is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and simplify the fraction.
For instance, the fraction 8/24 could be streamlined by solving 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 streamlined fraction of 1/3.
To see how this operates, let's utilize prime factorization to simplify the fraction 8/24. Foremost, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we cancel 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 remained with the streamlined fraction of 1/3.
Prime factorization additionally plays a crucial role in cryptography and computer science. As you progress in progressive mathematics and science theories, you will find additional uses for prime factorization and be pleased you are a pro.
It’s Prime Time to Boost Your Mathematical Skills
Prime factorization is a crucial concept in mathematics which allows us to streamline equations and fractions, moreover understand the characteristics of a value. By practicing and understanding the processes and utilizations of prime factorization, we can enhance our mathematical skills and problem-solving skills.
If you need help conquering prime factorization, contemplate connect with Grade Potential tutoring for expert assistance. Grade Potential instructors are skilled and educated in math. They could give customized learning and guidance to help you comprehend and apply prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could advance your mathematical skills, improve your confidence, and achieve your academic aims.
