Prime Factorization is a mathematical function used to break down 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, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify equations and fractions, in addition understand the properties of that number. Let’s take a closer look.
Methods for Figuring out 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. Both processes will grant you the exact outcome.
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.
Under it, make branches for the factors.
Continue drawing branches and factoring till you reach 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 would 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 comprehended by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next way for finding the prime factorization of a number is to initiate using a record of prime numbers. Note the number you are trying to factor. Next, divide the number by a prime number that divides evenly into it. It’s easiest to begin with the initial 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? Nope.
What is a prime number which 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 chart.
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 already worked by the means of a some examples, let’s do another one utilizing 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 test 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 done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has several practical uses in math. One of the main applications is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 can be streamlined by solving 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 simplified fraction of 1/3.
To check how this operates, 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 among 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 remained with the streamlined fraction of 1/3.
Prime factorization additionally plays an essential role in cryptography and computer science. As you proceed in advanced mathematics and science studies, you will figure out further utilizations for prime factorization and be delighted you are an expert.
It’s the Best Time to Boost Your Math Abilities
Prime factorization is an important theory in mathematics which allows us to streamline equations and fractions, also get a grasp of the characteristics of a value. By practicing and understanding the processes and uses of prime factorization, we can improve our mathematical skills and problem-solving abilities.
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