Prime Factorization is a mathematical method employed to break down a composite number into its prime factors. Composite numbers can be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can simplify fractions and equations, as well as understand the properties of that number. Let’s look closely.
Processes for Finding Prime Factorization
There are two major methods for performing prime factorization. You could utilize a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will give you the same answer.
Factor Tree Method
The initial method is utilizing a factor tree. To make a factor tree:
Start by noting the number you are attempting to factor at the top of the page.
Below it, create branches for the factors.
Continue drawing branches and factoring till you arrive at a prime number.
Here’s an example of the thinking 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 envision this process, we could create a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next process for finding the prime factorization of a number is to initiate using a record of prime numbers. Note down the number you are attempting to factor. Subsequently, divide the number by a prime number which divides equally into it. It’s easiest to initiate 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 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? Nope.
What is a prime number which 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 visualization.
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 previously worked through a few examples, let’s do one more using both methods.
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 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? 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 done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has several practical applications in math. One of the major utilizations is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 can be streamlined by working out 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 streamlined fraction of 1/3.
To see how this functions, let's use prime factorization to simplify the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, 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 also executes a crucial part in cryptography and computer science. As you go ahead in progressive math and science concepts, you will figure out more applications for prime factorization and be delighted you are an expert.
It’s Prime Time to Boost Your Math Abilities
Prime factorization is a crucial theory in mathematics which enables us to simplify equations and fractions, moreover learn the properties of a number. By practicing and understanding the methods and uses of prime factorization, we can enhance our math skills and problem-solving abilities.
If you need help conquering prime factorization, contemplate reaching out to Grade Potential tutoring for expert support. Grade Potential teachers are skilled and educated in mathematics. They could give customized learning and guidance to support you comprehend and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can improve your mathematical abilities, improve your confidence, and attain your academic objectives.
