Prime Factorization is a mathematical method used to segregate 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 only be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By figuring out the prime factors of a number, we could streamline fractions and equations, as well as understand the characteristics of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two primary ways for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. Both techniques will yield you the same answer.
Factor Tree Method
The first way is using a factor tree. To create a factor tree:
Start by noting the number you are trying to factor at the start of the page.
Below it, make branches for the factors.
Continue drawing branches and factoring until you arrive at 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this method, we can create a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for figuring out the prime factorization of a number is to start utilizing a list of prime numbers. Note the value you are trying to factor. Subsequently, divide the value by a prime number that 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 process 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? No.
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.
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 through a few examples, let’s do another one using both methods.
Let’s use a factor tree to figure out the prime factorization of 100.
We know 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 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has multiple real-life applications in math. One of the main applications is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and simplify the fraction.
For example, the fraction 8/24 can 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 simplify the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we rule 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 executes an essential role in cryptography and computer science. As you progress in sophisticated mathematics and science theories, you will find further uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Advance Your Math Skills
Prime factorization is a crucial concept in mathematics that enables us to streamline equations and fractions, moreover learn the properties of a number. By practicing and comprehending the processes and utilizations of prime factorization, we can improve our mathematical skills and analytical abilities.
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