Prime Factorization is a mathematical method used to segregate a composite number into its prime factors. Composite numbers can 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, in addition understand the characteristics of that number. Let’s look closely.
Methods for Figuring out Prime Factorization
There are two primary ways for figuring out prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. Both processes will give you the same answer.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Initiate by noting the value you are attempting to factor at the start of the page.
Underneath, make branches for the factors.
Continue creating branches and factoring till you attain 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 have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this procedure, we can make a factor tree for 36 as follows.
As you can see, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for finding the prime factorization of a number is to initiate utilizing a list of prime numbers. Note the number you are attempting to factor. Subsequently, divide the value by a prime number which divides evenly into it. It’s easiest to begin 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 which 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked through a few examples, let’s do another one employing 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 try 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? Nope.
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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has multiple realistic uses in mathematics. One of the primary uses is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For instance, the fraction 8/24 can be simplified by finding 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 clarified fraction of 1/3.
To check how this operates, 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 ever common prime factors within 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 remained with the simplified fraction of 1/3.
Prime factorization further executes an important part in computer science and cryptography. As you proceed in progressive mathematics and science concepts, you will figure out additional applications for prime factorization and be glad you are an expert.
It’s Peak Hour to Boost Your Mathematical Skills
Prime factorization is a crucial concept in mathematics which enables us to streamline equations and fractions, as well as understand the properties of a number. By practicing and comprehending the processes and applications of prime factorization, we can enhance our mathematical abilities and analytical skills.
If you need assistance conquering prime factorization, contemplate reaching out to Grade Potential tutoring for professional assistance. Grade Potential teachers are skilled and educated in mathematics. They can offer personalized instruction and guidance to support you learn and apply prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could advance your math abilities, improve your confidence, and reach your academic goals.
