Prime Factorization is a mathematical method employed to segregate 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 just be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we could streamline equations and fractions, as well as understand the properties of that number. Let’s look closely.
Processes for Figuring out Prime Factorization
There are two main ways for performing prime factorization. You could use a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will grant you the exact answer.
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 drawing branches and factoring until 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 would be 2 x 2 x 3 x 3. To imagine this method, we can make a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next process for working out the prime factorization of a number is to begin utilizing a list of prime numbers. Write down the value you are trying to factor. Subsequently, divide the number by a prime number that divides equally into it. It’s most convenient to start with the first 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 which 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
Although we’ve already worked by the means of a few examples, let’s do another one using 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.
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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has several real-life utilizations in mathematics. One of the major applications is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 could be streamlined by finding the prime factorization of both numbers. 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 works, let's employ 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 rule out ever common prime factors among 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 further executes an essential part in cryptography and computer science. As you go ahead in advanced math and science studies, you will figure out more applications for prime factorization and be glad you are a pro.
It’s Peak Hour to Advance Your Mathematical Skills
Prime factorization is a crucial concept in math that allows us to simplify equations and fractions, also understand the properties of a number. By practicing and comprehending the methods and utilizations of prime factorization, we can improve our mathematical skills and problem-solving skills.
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With the assistance of Grade Potential tutoring, you could advance your math abilities, improve your confidence, and attain your academic aims.
