Prime Factorization is a mathematical method utilized to break down 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 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 equations and fractions, also learn the characteristics of that number. Let’s get a closer look.
Ways for Finding Prime Factorization
There are two main ways for working out prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. Both processes will yield you the same result.
Factor Tree Method
The first method is utilizing a factor tree. To create a factor tree:
Start by writing the value you are attempting to factor at the start of the page.
Under it, make branches for the factors.
Proceed by making branches and factoring till you attain a prime number.
Here’s an example of the thought 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 would be 2 x 2 x 3 x 3. To visualize this process, we can create a factor tree for 36 as follows.
As demonstrated, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second method for finding the prime factorization of a number is to initiate using a record of prime numbers. Write down the value you are attempting to factor. Next, divide the number by a prime number which divides evenly into it. It’s simplest to start with the first few prime numbers, like 2, 3, and 5.
Let’s use the division process 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 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 established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve already worked by the means of a few examples, let’s do another one employing both processes.
Let’s utilize 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 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? Nope.
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 realistic utilizations in mathematics. One of the primary uses is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and simplify the fraction.
For instance, 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 canceling out the common prime factor of 2, we are left with the clarified fraction of 1/3.
To see how this operates, let's use prime factorization to streamline the fraction 8/24. Foremost, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out ever common prime factors within 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 plays a crucial role in computer science and cryptography. As you progress in sophisticated mathematics and science concepts, you will figure out more applications for prime factorization and be pleased you are a pro.
It’s Prime Time to Boost Your Mathematical Abilities
Prime factorization is a crucial concept in math which enables us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and understanding the processes and utilizations of prime factorization, we can enhance our mathematical skills and analytical abilities.
If you require help mastering prime factorization, contemplate contacting with Grade Potential tutoring for professional assistance. Grade Potential instructors are experienced and educated in mathematics. They could offer customized learning and guidance to support you understand and apply prime factorization in your studies.
With the support of Grade Potential tutoring, you could improve your mathematical abilities, improve your confidence, and attain your academic objectives.
