Prime Factorization is a mathematical function used to segregate 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 example 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can streamline fractions and equations, in addition understand the properties of that number. Let’s take a closer look.
Processes for Determining Prime Factorization
There are two main processes for working out prime factorization. You could employ a factor tree, or you can factor by dividing by prime numbers. Both methods will give you the same outcome.
Factor Tree Method
The primary method is utilizing a factor tree. To make a factor tree:
Start by noting the value you are trying to factor at the start of the page.
Underneath, make branches for the factors.
Continue creating branches and factoring until you reach a prime number.
Here’s an instance 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 would be 2 x 2 x 3 x 3. To visualize this procedure, we can make a factor tree for 36 as ensues.
As you can see, 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 start using a list of prime numbers. Note down the number you are trying to factor. Then, divide the value by a prime number that divides evenly into it. It’s easiest to initiate 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? No.
What is a prime number that 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.
Using 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 previously worked through a some examples, let’s do another one employing both processes.
Let’s use a factor tree to figure 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 here.
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? Nope.
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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has multiple practical utilizations in math. One of the primary utilizations is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and simplify the fraction.
For example, the fraction 8/24 can be simplified 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 streamlined 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 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 additionally executes an important role in cryptography and computer science. As you proceed in advanced mathematics and science studies, you will figure out further applications for prime factorization and be delighted you are a pro.
It’s Peak Hour to Boost Your Mathematical Abilities
Prime factorization is a crucial theory in math which allows us to streamline equations and fractions, moreover get a grasp of the characteristics of a value. By practicing and comprehending the processes and uses of prime factorization, we can improve our math abilities and analytical abilities.
If you need assistance mastering prime factorization, contemplate contacting with Grade Potential tutoring for expert assistance. Grade Potential teachers are skilled and knowledgeable in mathematics. They can offer customized learning and support to help you learn and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you could advance your mathematical skills, boost your confidence, and achieve your academic aims.
