Prime Factorization is a mathematical method used to segregate a composite number into its prime factors. Composite numbers could 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 finding the prime factors of a number, we can streamline fractions and equations, in addition learn the characteristics of that number. Let’s get a closer look.
Ways for Finding Prime Factorization
There are two main methods for working out prime factorization. You could utilize a factor tree, or you could factor by dividing by prime numbers. Both processes will grant you the exact outcome.
Factor Tree Method
The initial method is using a factor tree. To create a factor tree:
Start by writing the value you are attempting to factor at the top of the page.
Underneath, create branches for the factors.
Continue making branches and factoring until you arrive at a prime number.
Here’s an example 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 visualize this method, we could make a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next process for working out the prime factorization of a number is to initiate utilizing a record of prime numbers. Note down the number you are trying to factor. Next, divide the value by a prime number which divides evenly into it. It’s simplest to start 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 that divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? Nope.
What is a prime number which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
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 depiction.
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 earlier worked through a some examples, let’s do one more employing both processes.
Let’s utilize a factor tree to find 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 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 that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number that 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.
Applications of Prime Factorization
Prime factorization has multiple practical uses in mathematics. One of the main applications is streamlining fractions. By working 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 can be streamlined 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 streamlined fraction of 1/3.
To see how this operates, let's employ prime factorization to simplify the fraction 8/24. First, 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 among 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 plays an essential role in cryptography and computer science. As you progress in sophisticated mathematics and science studies, you will find more applications for prime factorization and be pleased you are a professional.
It’s Prime Time to Boost Your Mathematical Skills
Prime factorization is an important concept in math that enables us to simplify equations and fractions, as well as get a grasp of the properties of a number. By practicing and comprehending the processes and applications of prime factorization, we could improve our mathematical abilities and analytical abilities.
If you need assistance mastering prime factorization, contemplate contacting with Grade Potential tutoring for expert assistance. Grade Potential tutors are skilled and knowledgeable in mathematics. They could provide customized learning and assistance to help you learn and apply prime factorization in your studies.
With the assistance of Grade Potential tutoring, you can improve your mathematical abilities, boost your confidence, and achieve your academic goals.
