Prime Factorization is a mathematical function used to segregate a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can just be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify fractions and equations, in addition understand the characteristics of that number. Let’s look closely.
Methods for Figuring out Prime Factorization
There are two primary methods 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 yield you the same answer.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Begin by noting the number you are attempting to factor at the top of the page.
Under it, make branches for the factors.
Continue making branches and factoring until you attain 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 are done.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine 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, which are 2 * 3 * 2 * 3.
Division Method
The next process for figuring out the prime factorization of a number is to begin using a list of prime numbers. Write down the number you are attempting to factor. Then, divide the number by a prime number which divides equally into it. It’s simplest to start with the first few prime numbers, like 2, 3, and 5.
Let’s utilize the division method for prime factorization of 36.
What is a prime number which 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a chart.
Using both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked by the means of a some examples, let’s do another one utilizing both processes.
Let’s use 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 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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has multiple real-life applications in math. One of the primary applications is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and simplify the fraction.
For example, the fraction 8/24 can be simplified by finding 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 clarified fraction of 1/3.
To check how this works, 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
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 remained with the streamlined fraction of 1/3.
Prime factorization further plays an essential part in computer science and cryptography. As you proceed in progressive math and science theories, you will figure out more utilizations for prime factorization and be glad you are a pro.
It’s Prime Time to Enhance Your Math Skills
Prime factorization is an important concept in mathematics that allows us to streamline equations and fractions, as well as learn the characteristics of a number. By practicing and understanding the methods and applications of prime factorization, we could improve our mathematical skills and problem-solving abilities.
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With the assistance of Grade Potential tutoring, you can advance your mathematical skills, boost your confidence, and reach your academic objectives.
