Prime Factorization is a mathematical method employed to break down 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, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could streamline equations and fractions, also understand the characteristics of that number. Let’s get a closer look.
Processes for Finding Prime Factorization
There are two major ways for figuring out prime factorization. You can employ a factor tree, or you can factor by dividing by prime numbers. One as well as the other techniques will grant you the same outcome.
Factor Tree Method
The primary way is utilizing a factor tree. To create a factor tree:
Initiate by writing the value you are attempting to factor at the top of the page.
Below it, create branches for the factors.
Continue making branches and factoring till you attain a prime number.
Here’s an example of the thinking process:
We understand 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 envision this method, we can create a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second process for figuring out the prime factorization of a number is to begin using a record of prime numbers. Write down the value you are attempting to factor. Next, divide the value by a prime number that divides evenly into it. It’s most convenient to start with the initial few prime numbers, like 2, 3, and 5.
Let’s use 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? 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 visualization.
Using both systems, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve already worked through a few examples, let’s do another one employing both methods.
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 clear.
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 which divides into 100? 2 * 50 = 100
Is 50 a prime number? No.
What is a prime number which divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
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 many practical uses in math. One of the primary utilizations is streamlining 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 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
Subsequently, we rule out ever common prime factors among 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 simplified fraction of 1/3.
Prime factorization additionally plays an essential part in computer science and cryptography. As you progress in advanced math and science theories, you will figure out additional applications for prime factorization and be delighted you are a professional.
It’s Peak Hour to Enhance Your Mathematical Abilities
Prime factorization is an essential concept in math that allows us to simplify equations and fractions, as well as learn the characteristics of a value. By practicing and understanding the processes and applications of prime factorization, we can improve our math abilities and analytical skills.
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With the assistance of Grade Potential tutoring, you could advance your math skills, improve your confidence, and attain your academic goals.
