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 example 2, 3, 5, and 7.
By working 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.
Ways for Figuring out Prime Factorization
There are two major processes for working out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other techniques will grant you the exact outcome.
Factor Tree Method
The initial way is utilizing a factor tree. To create a factor tree:
Begin by writing the value you are trying to factor at the top of the page.
Under it, create branches for the factors.
Proceed by making branches and factoring before 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 are done here.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To visualize this method, we could 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 process for working out the prime factorization of a number is to start utilizing a record of prime numbers. Write down the value you are trying to factor. Then, divide the value by a prime number that divides evenly into it. It’s simplest to begin with the first few prime numbers, like 2, 3, and 5.
Let’s use 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 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 process, we found 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 one more using 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s test 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 which 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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has several real-life uses in math. One of the major applications is streamlining fractions. By finding 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 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 streamlined fraction of 1/3.
To see how this functions, let's employ 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
Next, we rule out ever 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 further executes an essential role in cryptography and computer science. As you progress in sophisticated math and science theories, you will find further applications for prime factorization and be delighted you are an expert.
It’s the Best Time to Boost Your Math Abilities
Prime factorization is an essential theory in math that allows us to simplify equations and fractions, also understand the properties of a number. By practicing and understanding the methods and utilizations of prime factorization, we could improve our math skills and problem-solving skills.
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