Prime Factorization is a mathematical function utilized to segregate a composite number into its prime factors. Composite numbers can 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 example 2, 3, 5, and 7.
By working out the prime factors of a number, we can simplify equations and fractions, as well as learn the characteristics of that number. Let’s take a closer look.
Ways for Figuring out Prime Factorization
There are two major methods for figuring out prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. Both methods will grant you the exact answer.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Begin by writing the number you are trying to factor at the top of the page.
Under it, create branches for the factors.
Continue making branches and factoring until you arrive at a prime number.
Here’s an instance of the thought process:
We know 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 method, we can make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second way for finding the prime factorization of a number is to begin utilizing a record of prime numbers. Note the number you are attempting to factor. Then, divide the number by a prime number which divides evenly into it. It’s easiest to begin 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? No.
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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both methods, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked by the means of a few examples, let’s do another one 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 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 which 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 multiple real-life uses in mathematics. One of the primary uses 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 instance, the fraction 8/24 could be simplified by solving the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling 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. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we rule out ever 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 left with the streamlined fraction of 1/3.
Prime factorization also plays an essential part in cryptography and computer science. As you progress in sophisticated mathematics and science theories, you will figure out further utilizations for prime factorization and be glad you are a pro.
It’s Prime Time to Enhance Your Mathematical Skills
Prime factorization is an essential concept in math which allows us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and understanding the methods and utilizations of prime factorization, we can enhance our math skills and analytical abilities.
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With the assistance of Grade Potential tutoring, you could enhance your mathematical skills, boost your confidence, and achieve your academic objectives.
