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, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we can streamline equations and fractions, in addition learn the properties of that number. Let’s take a closer look.
Methods for Figuring out Prime Factorization
There are two primary processes for figuring out prime factorization. You can employ a factor tree, or you can factor by dividing by prime numbers. Both methods will give you the same outcome.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Start by writing the number you are trying to factor at the top of the page.
Under it, create branches for the factors.
Proceed by creating branches and factoring till you reach a prime number.
Here’s an example 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 here.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To visualize this method, we could create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next method for finding the prime factorization of a number is to initiate utilizing a record of prime numbers. Note down the value you are attempting to factor. Then, divide the number by a prime number that divides equally into it. It’s most convenient 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 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? No.
What is a prime number which 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 chart.
Using both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve earlier worked by the means of a few examples, let’s do one more employing both methods.
Let’s utilize 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 try the division process:
What is the prime factorization for 100?
What is a prime number that 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? Nope.
What is a prime number which 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.
Uses of Prime Factorization
Prime factorization has multiple practical utilizations in mathematics. One of the major applications is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline the fraction.
For example, the fraction 8/24 can be simplified by solving 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 use prime factorization to streamline the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we rule out any common prime factors between 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 computer science and cryptography. As you proceed in progressive mathematics and science studies, you will find further applications for prime factorization and be delighted you are an expert.
It’s Prime Time to Boost Your Math Skills
Prime factorization is an essential theory in mathematics that allows us to streamline equations and fractions, also learn the properties of a value. By practicing and comprehending the methods and applications of prime factorization, we could 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 tutors are skilled and knowledgeable in mathematics. They could give customized learning and guidance to help you learn and utilize prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could advance your mathematical skills, boost your confidence, and achieve your academic aims.
