Prime Factorization is a mathematical method utilized 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, for example 2, 3, 5, and 7.
By figuring out the prime factors of a number, we could streamline equations and fractions, also understand the characteristics of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two primary ways for figuring out prime factorization. You can use a factor tree, or you can factor by dividing by prime numbers. Both processes will give you the exact answer.
Factor Tree Method
The first way is using a factor tree. To make a factor tree:
Start by writing the value you are attempting to factor at the top of the page.
Under it, create branches for the factors.
Continue creating branches and factoring before you reach a prime number.
Here’s an instance 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 method, we can create a factor tree for 36 as follows.
As demonstrated, the prime factorization of 36 is comprehended by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next method for figuring out the prime factorization of a number is to initiate using a list of prime numbers. Note the value you are trying to factor. Then, divide the number 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? 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.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a chart.
Using both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a few 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 done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try the division method:
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.
Uses of Prime Factorization
Prime factorization has many realistic uses in math. One of the main applications is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 could be simplified by finding the prime factorization of both values. 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 check how this operates, let's use prime factorization to simplify 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 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 executes a crucial part in computer science and cryptography. As you go ahead in sophisticated mathematics and science studies, you will find more utilizations for prime factorization and be delighted you are a professional.
It’s Prime Time to Boost Your Math Abilities
Prime factorization is an essential concept in mathematics that allows us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and understanding the methods and utilizations of prime factorization, we could enhance our math abilities and problem-solving skills.
If you need support conquering prime factorization, contemplate reaching out to Grade Potential tutoring for professional support. Grade Potential teachers are skilled and knowledgeable in math. They can provide personalized instruction and assistance to help you understand and apply prime factorization in your studies.
With the support of Grade Potential tutoring, you can enhance your math abilities, improve your confidence, and achieve your academic objectives.
