Prime Factorization is a mathematical method employed to segregate 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 just 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, also learn the properties of that number. Let’s take a closer look.
Processes for Determining Prime Factorization
There are two major methods for figuring out prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will yield you the same result.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Begin by noting the value you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by making branches and factoring till you arrive at 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 will be 2 x 2 x 3 x 3. To visualize this procedure, we could make a factor tree for 36 as follows.
As you can see, 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 process for finding the prime factorization of a number is to start using a list of prime numbers. Note the value you are trying to factor. Subsequently, divide the value by a prime number that divides equally into it. It’s easiest to start with the first few prime numbers, like 2, 3, and 5.
Let’s utilize 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? 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 chart.
Using both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve earlier worked through a some examples, let’s do another one using both methods.
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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try the division method:
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 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has multiple practical utilizations in mathematics. 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 streamline the fraction.
For instance, the fraction 8/24 could be streamlined by finding the prime factorization of both values. 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 functions, let's use prime factorization to streamline the fraction 8/24. Primarily, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we cancel out any common prime factors between 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 further executes an important part in computer science and cryptography. As you proceed in progressive mathematics and science concepts, you will find additional applications for prime factorization and be delighted you are an expert.
It’s the Best Time to Enhance Your Mathematical Abilities
Prime factorization is an essential theory in mathematics which allows us to simplify equations and fractions, as well as learn the characteristics of a value. By practicing and comprehending the methods and utilizations of prime factorization, we can enhance our mathematical abilities and analytical abilities.
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With the support of Grade Potential tutoring, you could enhance your mathematical abilities, boost your confidence, and attain your academic goals.
