Prime Factorization is a mathematical function utilized to segregate 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 instance 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can simplify equations and fractions, also learn the characteristics of that number. Let’s get a closer look.
Ways for Determining Prime Factorization
There are two primary processes for figuring out prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. Both processes will grant you the exact answer.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Initiate by noting the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring till you reach a prime number.
Here’s an instance of the thought process:
We recognize that 6 * 6 = 36.
Is 6 a prime number? No. 2 * 3 = 6.
Are 2 and 3 prime numbers? Yes. We have reached the end.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To visualize this procedure, we can create a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second method for finding the prime factorization of a number is to begin using a record of prime numbers. Note the value you are trying to factor. Next, divide the value by a prime number which divides equally into it. It’s simplest to begin 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 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.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Using both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked through a few examples, let’s do one more using both processes.
Let’s utilize a factor tree to work 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 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 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.
Utilizations of Prime Factorization
Prime factorization has multiple realistic utilizations in mathematics. One of the primary applications is streamlining fractions. By finding 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 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 clarified fraction of 1/3.
To see how this functions, let's use 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
Next, we rule out ever common prime factors between 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 streamlined fraction of 1/3.
Prime factorization also plays an important part in computer science and cryptography. As you proceed in advanced mathematics and science studies, you will figure out more uses for prime factorization and be glad you are a professional.
It’s Peak Hour to Enhance Your Mathematical Skills
Prime factorization is an essential concept in mathematics which allows us to simplify equations and fractions, also understand the properties of a value. By practicing and comprehending the processes and uses of prime factorization, we can improve our math abilities and problem-solving skills.
If you require assistance mastering prime factorization, consider connect with Grade Potential tutoring for professional support. Grade Potential tutors are skilled and knowledgeable in mathematics. They can give customized instruction and guidance to help you comprehend and utilize prime factorization in your studies.
With the assistance of Grade Potential tutoring, you can improve your math abilities, improve your confidence, and reach your academic objectives.
