Prime Factorization is a mathematical function employed 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 just be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify fractions and equations, as well as learn the properties of that number. Let’s take a closer look.
Processes for Determining Prime Factorization
There are two primary processes for performing prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will give you the exact result.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Begin by noting the number you are attempting to factor at the start of the page.
Underneath, create branches for the factors.
Proceed by making branches and factoring till you reach 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 have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this procedure, we could make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for working out the prime factorization of a number is to start using a list of prime numbers. Note the value you are attempting to factor. Subsequently, divide the value by a prime number that divides equally into it. It’s easiest to start with the initial 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? Nope.
What is a prime number which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
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.
Utilizing both systems, 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 use 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 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? Nope.
What is a prime number that 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 many real-life uses in math. One of the primary uses 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 clarify 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 canceling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To check how this works, let's employ 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
Subsequently, we cancel out ever common prime factors between 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 simplified fraction of 1/3.
Prime factorization additionally plays a crucial part in cryptography and computer science. As you proceed in advanced math and science theories, you will figure out additional uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Boost Your Math Abilities
Prime factorization is an essential theory in mathematics that enables us to simplify equations and fractions, also get a grasp of the characteristics of a value. By practicing and understanding the methods and utilizations of prime factorization, we could enhance our math abilities and analytical abilities.
If you require help mastering prime factorization, consider contacting with Grade Potential tutoring for professional assistance. Grade Potential tutors are skilled and knowledgeable in math. They could give personalized learning and assistance to support you learn and utilize prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could advance your mathematical abilities, boost your confidence, and reach your academic objectives.
