Prime Factorization is a mathematical method employed to split up 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, for example 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify fractions and equations, also learn the characteristics of that number. Let’s look closely.
Processes for Figuring out Prime Factorization
There are two primary ways for working out prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both methods will grant you the exact answer.
Factor Tree Method
The primary method is using a factor tree. To make a factor tree:
Start by writing the number you are trying to factor at the start of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring before you reach 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this method, we can make a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next process for figuring out the prime factorization of a number is to initiate using a record of prime numbers. Note down the number you are trying to factor. Subsequently, divide the value by a prime number which divides equally into it. It’s most convenient to start with the first few prime numbers, like 2, 3, and 5.
Let’s utilize 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? 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.
Using both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a some examples, let’s do one more using both processes.
Let’s utilize a factor tree to work out the prime factorization of 100.
We learned 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 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? 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.
Utilizations of Prime Factorization
Prime factorization has many realistic uses in mathematics. One of the main applications is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 could be streamlined by working out the prime factorization of both values. 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 utilize prime factorization to simplify 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 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 left with the streamlined fraction of 1/3.
Prime factorization also plays a crucial role in computer science and cryptography. As you proceed in sophisticated math and science studies, you will find additional uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Enhance Your Mathematical Skills
Prime factorization is an essential concept in math that enables us to streamline equations and fractions, as well as understand the properties of a number. By practicing and comprehending the processes and uses of prime factorization, we can enhance our math abilities and problem-solving skills.
If you require assistance conquering prime factorization, contemplate reaching out to Grade Potential tutoring for professional assistance. Grade Potential teachers are skilled and knowledgeable in math. They can give customized instruction and assistance to help you understand and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can improve your math abilities, improve your confidence, and reach your academic objectives.
