Prime Factorization is a mathematical function used to split up 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, as well as understand the characteristics of that number. Let’s look closely.
Ways for Figuring out Prime Factorization
There are two primary 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 methods will grant you the exact answer.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Start by writing the number you are trying to factor at the top of the page.
Underneath, create branches for the factors.
Continue creating branches and factoring till you arrive at a prime number.
Here’s an example of the thought 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 imagine this method, we could create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next process for finding the prime factorization of a number is to begin using a list of prime numbers. Write down the value you are attempting to factor. Then, divide the number by a prime number which divides evenly into it. It’s simplest to initiate with the initial 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? 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.
Using both methods, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a few examples, let’s do one more using both processes.
Let’s utilize a factor tree to figure 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 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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has many practical uses in math. One of the main applications 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 simplify the fraction.
For instance, 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 clarified fraction of 1/3.
To see how this works, let's utilize prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we rule 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 additionally executes an essential role in computer science and cryptography. As you proceed in advanced math and science theories, you will figure out additional applications for prime factorization and be pleased you are a professional.
It’s Peak Hour to Enhance Your Math Abilities
Prime factorization is an important concept in mathematics that enables us to streamline equations and fractions, moreover learn the properties of a number. By practicing and understanding the methods and utilizations of prime factorization, we can improve our math abilities and analytical skills.
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