Prime Factorization is a mathematical function utilized to break down 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, also understand the properties of that number. Let’s get a closer look.
Methods for Figuring out Prime Factorization
There are two major methods for figuring out prime factorization. You can use a factor tree, or you can factor by dividing by prime numbers. Both techniques will yield you the same outcome.
Factor Tree Method
The primary way is using a factor tree. To make a factor tree:
Initiate by writing the number you are attempting to factor at the start of the page.
Underneath, make branches for the factors.
Proceed by drawing branches and factoring till you arrive at 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 imagine this method, we could create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second method for finding the prime factorization of a number is to initiate utilizing a list of prime numbers. Note down the value you are attempting to factor. Subsequently, divide the value by a prime number that divides evenly into it. It’s most convenient 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? No.
What is a prime number that 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Using both methods, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve earlier worked through a some examples, let’s do another one utilizing both processes.
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 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? Nope.
What is a prime number which 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 several practical uses in mathematics. One of the major uses is streamlining 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 could be streamlined 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 simplified fraction of 1/3.
To see how this operates, let's use prime factorization to simplify the fraction 8/24. Primarily, 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 among 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 also plays a crucial part in computer science and cryptography. As you go ahead in progressive math and science studies, you will figure out more applications for prime factorization and be delighted you are a pro.
It’s the Best Time to Enhance Your Math Skills
Prime factorization is an important theory in mathematics that allows us to streamline equations and fractions, as well as get a grasp of the properties of a number. By practicing and understanding the processes and applications of prime factorization, we can enhance our mathematical abilities and analytical skills.
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