Prime Factorization is a mathematical method used to split up a composite number into its prime factors. Composite numbers could 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, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify fractions and equations, also understand the properties of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two major 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 methods will yield you the same answer.
Factor Tree Method
The initial method is using a factor tree. To make a factor tree:
Start by writing the value you are trying to factor at the top of the page.
Under it, make branches for the factors.
Proceed by creating branches and factoring until you reach a prime number.
Here’s an instance of the thought process:
We know 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 procedure, we can create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for figuring out the prime factorization of a number is to start utilizing a record of prime numbers. Note down the value you are trying to factor. Then, divide the value by a prime number which divides equally into it. It’s simplest to begin 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 that divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? No.
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.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both systems, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve previously worked through a few examples, let’s do another one using both processes.
Let’s use 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 test 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 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 uses in math. One of the primary 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 instance, the fraction 8/24 could be streamlined by finding 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 see how this operates, 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
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 canceling out the common prime factors of 2, we are left with the streamlined fraction of 1/3.
Prime factorization additionally plays an essential role in cryptography and computer science. As you progress in progressive mathematics and science theories, you will figure out more applications for prime factorization and be delighted you are a professional.
It’s Prime Time to Enhance Your Mathematical Abilities
Prime factorization is an important theory in math that enables us to simplify equations and fractions, moreover get a grasp of the characteristics of a number. By practicing and comprehending the methods and uses of prime factorization, we could enhance our mathematical abilities and analytical abilities.
If you require assistance mastering prime factorization, consider reaching out to Grade Potential tutoring for professional assistance. Grade Potential instructors are skilled and knowledgeable in math. They could give personalized learning and guidance to help you learn and utilize prime factorization in your studies.
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