Prime Factorization is a mathematical function 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, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we can streamline equations and fractions, as well as learn the properties of that number. Let’s get a closer look.
Methods for Determining Prime Factorization
There are two primary processes for performing prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will yield you the same result.
Factor Tree Method
The primary method is utilizing a factor tree. To make a factor tree:
Start by noting the value you are attempting to factor at the top of the page.
Below it, make branches for the factors.
Proceed by making branches and factoring till you arrive at a prime number.
Here’s an example of the thinking 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this method, we can make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is figured out 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 record of prime numbers. Note down the number you are trying to factor. Next, divide the value by a prime number which 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 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 which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? No.
What is a prime number which 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
Despite the fact that we’ve previously worked by the means of a some examples, let’s do one more using both methods.
Let’s utilize a factor tree to find 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 done here.
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 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? 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.
Utilizations of Prime Factorization
Prime factorization has multiple real-life applications in mathematics. One of the major applications is streamlining fractions. By finding out 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 numbers. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling out the common prime factor of 2, we are left with the streamlined fraction of 1/3.
To see how this works, let's employ prime factorization to streamline the fraction 8/24. Foremost, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we rule out ever common prime factors within the numerator and denominator.
8/24 = 2 * 2 * 2 / 2 * 2 * 2 * 3 = 1/3
After ruling out the common prime factors of 2, we are left with the streamlined fraction of 1/3.
Prime factorization further plays an essential part in cryptography and computer science. As you go ahead in sophisticated mathematics and science studies, you will figure out further uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Enhance Your Math Abilities
Prime factorization is an important concept in mathematics which allows us to streamline equations and fractions, moreover learn the properties of a number. By practicing and understanding the processes and utilizations of prime factorization, we could improve our mathematical skills and problem-solving abilities.
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