Prime Factorization is a mathematical method employed 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 only 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, in addition learn the properties of that number. Let’s take a closer look.
Processes for Determining Prime Factorization
There are two major methods for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. Both techniques will grant you the same answer.
Factor Tree Method
The first method is utilizing a factor tree. To make a factor tree:
Initiate by noting the value you are attempting to factor at the top of the page.
Below it, make branches for the factors.
Proceed by creating branches and factoring until you arrive at a prime number.
Here’s an instance 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.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this method, we could create a factor tree for 36 as ensues.
As you can see, 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 second way for finding the prime factorization of a number is to begin utilizing a list of prime numbers. Write down the number you are trying to factor. Subsequently, divide the value by a prime number which divides equally into it. It’s easiest 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? 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a chart.
Using both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked by the means of a some examples, let’s do one more employing both processes.
Let’s use a factor tree to find the prime factorization of 100.
We know 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 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.
Uses of Prime Factorization
Prime factorization has many realistic uses in math. One of the major utilizations is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For example, the fraction 8/24 could be simplified 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 check how this functions, 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
Then, we rule out any common prime factors among 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 simplified fraction of 1/3.
Prime factorization further executes a crucial part in computer science and cryptography. As you go ahead in sophisticated math and science concepts, you will find further applications for prime factorization and be delighted you are an expert.
It’s Peak Hour to Boost Your Math Abilities
Prime factorization is a crucial theory in mathematics which enables us to streamline equations and fractions, moreover understand the characteristics of a number. By practicing and understanding the processes and utilizations of prime factorization, we could improve our mathematical skills and analytical abilities.
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