Prime Factorization is a mathematical function used to break down a composite number into its prime factors. Composite numbers can 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, for instance 2, 3, 5, and 7.
By finding the prime factors of a number, we could streamline equations and fractions, also learn the properties of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two major processes for performing prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will yield you the exact outcome.
Factor Tree Method
The initial way is utilizing a factor tree. To create a factor tree:
Begin by noting the number you are trying to factor at the start of the page.
Underneath, create branches for the factors.
Continue creating branches and factoring until you reach a prime number.
Here’s an example of the thinking 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this procedure, we could make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for figuring out the prime factorization of a number is to initiate using a record of prime numbers. Note down the value you are trying to factor. Subsequently, divide the value by a prime number that divides evenly into it. It’s simplest to initiate with the first 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? No.
What is a prime number which 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.
Utilizing both systems, 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 one more utilizing both methods.
Let’s use 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 done.
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 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.
Uses of Prime Factorization
Prime factorization has several real-life uses in math. One of the main uses 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 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 see how this operates, let's employ prime factorization to simplify the fraction 8/24. Primarily, 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 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 a crucial role in computer science and cryptography. As you go ahead in progressive math and science concepts, you will figure out more utilizations for prime factorization and be delighted you are an expert.
It’s Prime Time to Enhance Your Mathematical Skills
Prime factorization is an important concept in mathematics that allows us to simplify equations and fractions, also understand the characteristics of a value. By practicing and understanding the methods and utilizations of prime factorization, we can enhance our mathematical abilities and problem-solving abilities.
If you need assistance mastering prime factorization, contemplate reaching out to Grade Potential tutoring for expert support. Grade Potential instructors are experienced and knowledgeable in math. They could give customized learning and guidance to help you comprehend and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can enhance your math skills, improve your confidence, and attain your academic aims.
