Prime Factorization is a mathematical method employed to split up a composite number into its prime factors. Composite numbers can be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can only be divided by 1 and themselves, for example 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify equations and fractions, as well as learn the characteristics of that number. Let’s get a closer look.
Ways for Finding Prime Factorization
There are two primary methods for figuring out prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both processes will give you the same outcome.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Initiate by noting the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring before you reach 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 will be 2 x 2 x 3 x 3. To envision this method, we can make a factor tree for 36 as ensues.
As demonstrated, 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 second process for figuring out 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 begin 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 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 depiction.
Using both methods, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve already worked by the means of a few examples, let’s do another one using 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 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? Nope.
What is a prime number that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number which 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.
Uses of Prime Factorization
Prime factorization has many practical uses in math. One of the primary uses is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For instance, the fraction 8/24 can be streamlined 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 works, let's use prime factorization to streamline the fraction 8/24. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we cancel out any 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 executes an important role in computer science and cryptography. As you go ahead in advanced mathematics and science theories, you will figure out more applications for prime factorization and be delighted you are a pro.
It’s the Best Time to Advance Your Mathematical Abilities
Prime factorization is an important theory in mathematics which enables us to streamline equations and fractions, moreover learn the properties of a number. By practicing and comprehending the processes and applications of prime factorization, we can improve our math skills and problem-solving skills.
If you require support mastering prime factorization, consider contacting with Grade Potential tutoring for professional support. Grade Potential instructors are experienced and knowledgeable in math. They can offer personalized instruction and guidance to support you comprehend and apply prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could improve your mathematical abilities, improve your confidence, and reach your academic goals.
