Prime Factorization is a mathematical function employed to split up 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, for example 2, 3, 5, and 7.
By finding the prime factors of a number, we could streamline equations and fractions, in addition learn the properties of that number. Let’s get a closer look.
Processes for Determining Prime Factorization
There are two main ways for figuring out prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. Both techniques will grant you the exact outcome.
Factor Tree Method
The first method is using a factor tree. To make a factor tree:
Begin by noting the value you are trying to factor at the start of the page.
Below it, create branches for the factors.
Proceed by making branches and factoring until you arrive at 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To visualize this procedure, we can create 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. Note the number you are attempting to factor. Next, 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 use 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? Nope.
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 depiction.
Using both systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked by the means of a few examples, let’s do one more utilizing both processes.
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 try the division method:
What is the prime factorization for 100?
What is a prime number that divides into 100? 2 * 50 = 100
Is 50 a prime number? Nope.
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 done here.
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 primary applications 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 solving 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 operates, let's employ prime factorization to streamline 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 rule out any common prime factors within 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 remained with the simplified fraction of 1/3.
Prime factorization additionally plays an important part in computer science and cryptography. As you proceed in progressive math and science concepts, you will find additional applications for prime factorization and be delighted you are a professional.
It’s Prime Time to Boost Your Math Skills
Prime factorization is an essential theory in mathematics which allows us to streamline equations and fractions, also understand the properties of a number. By practicing and comprehending the methods and uses of prime factorization, we could improve our mathematical abilities and problem-solving abilities.
If you require help mastering prime factorization, contemplate contacting with Grade Potential tutoring for expert support. Grade Potential tutors are skilled and knowledgeable in math. They could give personalized learning and support to support you understand and apply prime factorization in your studies.
With the help of Grade Potential tutoring, you could improve your mathematical abilities, improve your confidence, and reach your academic objectives.
