Prime Factorization is a mathematical method employed to split up a composite number into its prime factors. Composite numbers could 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, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we can simplify equations and fractions, also understand the characteristics of that number. Let’s get a closer look.
Ways for Determining Prime Factorization
There are two main processes for working out prime factorization. You could use a factor tree, or you can factor by dividing by prime numbers. Both processes will give you the exact answer.
Factor Tree Method
The first method is using a factor tree. To create a factor tree:
Start by noting the number you are trying to factor at the top of the page.
Below it, create branches for the factors.
Proceed by creating branches and factoring until you arrive at a prime number.
Here’s an example of the thought 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this procedure, we could create a factor tree for 36 as follows.
Consequently, 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 way for figuring out the prime factorization of a number is to initiate utilizing a list of prime numbers. Write down the value you are attempting to factor. Next, 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 use 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 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 depiction.
Utilizing both process, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve earlier worked by the means of a some examples, let’s do another one utilizing both methods.
Let’s utilize a factor tree to work 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 done.
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 that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number that divides into 25? 5 * 5 = 25
Is 5 a prime number? Yes. We are done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has multiple practical 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 clarify the fraction.
For example, the fraction 8/24 can be simplified by solving the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By ruling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To see how this functions, let's employ prime factorization to streamline the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we cancel out any 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 remained with the streamlined fraction of 1/3.
Prime factorization further plays a crucial part in computer science and cryptography. As you go ahead in advanced mathematics and science theories, you will find further uses for prime factorization and be glad you are a professional.
It’s Prime Time to Boost Your Mathematical Abilities
Prime factorization is an essential theory in math that allows us to simplify equations and fractions, also learn the characteristics of a number. By practicing and comprehending the processes and applications of prime factorization, we could improve our mathematical skills and problem-solving abilities.
If you need assistance mastering prime factorization, consider connect with Grade Potential tutoring for expert support. Grade Potential instructors are experienced and educated in mathematics. They could give personalized instruction and guidance to support you understand and apply prime factorization in your studies.
With the help of Grade Potential tutoring, you can enhance your math abilities, boost your confidence, and attain your academic goals.
