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 conclude 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 streamline equations and fractions, also learn the characteristics of that number. Let’s look closely.
Ways for Determining Prime Factorization
There are two main methods for figuring out prime factorization. You could use a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will give you the same outcome.
Factor Tree Method
The initial method is utilizing a factor tree. To create a factor tree:
Begin by writing the number you are trying to factor at the start of the page.
Underneath, make branches for the factors.
Proceed by making branches and factoring till 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 have reached the end.
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 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 method 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. Next, divide the value by a prime number which divides evenly into it. It’s most convenient to begin with the first few prime numbers, like 2, 3, and 5.
Let’s use 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 that divides into 9? 3 → 3 * 3 = 9
Is 3 a prime number? Yes. We are done.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve already worked through a few examples, let’s do one more employing both processes.
Let’s utilize 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? Nope.
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.
Uses of Prime Factorization
Prime factorization has multiple practical applications in math. One of the main utilizations is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline the fraction.
For example, the fraction 8/24 can 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 simplified fraction of 1/3.
To check how this functions, let's use prime factorization to streamline the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we cancel out any 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 also executes an essential role in computer science and cryptography. As you proceed in sophisticated mathematics and science studies, you will figure out further utilizations for prime factorization and be pleased you are a professional.
It’s Peak Hour to Boost Your Math Abilities
Prime factorization is an important theory in math which allows us to simplify equations and fractions, moreover understand the characteristics of a number. By practicing and understanding the methods and applications of prime factorization, we can enhance our mathematical abilities and analytical skills.
If you require help conquering prime factorization, contemplate contacting with Grade Potential tutoring for professional support. Grade Potential teachers are experienced and educated in math. They could offer personalized instruction and support to help you learn and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can improve your math abilities, boost your confidence, and reach your academic aims.
