Prime Factorization is a mathematical function used to break down a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to result in a whole number. Prime numbers can just be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify fractions and equations, in addition understand the properties of that number. Let’s get a closer look.
Processes for Finding Prime Factorization
There are two major methods for figuring out prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will give you the same result.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Initiate by noting the number you are trying to factor at the top of the page.
Under it, create branches for the factors.
Continue making branches and factoring before you reach 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 are done.
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 at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for working out the prime factorization of a number is to initiate utilizing a list of prime numbers. Note the value you are trying to factor. Next, divide the value by a prime number which divides evenly into it. It’s simplest 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 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 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 visualization.
Using both methods, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked by the means of a some examples, let’s do another one employing both methods.
Let’s utilize 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 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? No.
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 done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has several real-life applications in mathematics. One of the major applications is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline the fraction.
For instance, the fraction 8/24 could be streamlined by working out the prime factorization of both numbers. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling out the common prime factor of 2, we are left with the clarified fraction of 1/3.
To see how this operates, let's employ prime factorization to simplify the fraction 8/24. First, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, 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 remained with the simplified fraction of 1/3.
Prime factorization additionally plays an essential role in computer science and cryptography. As you progress in sophisticated math and science theories, you will figure out additional applications for prime factorization and be glad you are a pro.
It’s the Best Time to Boost Your Mathematical Skills
Prime factorization is an essential concept in math that enables us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and understanding the methods and utilizations of prime factorization, we could enhance our mathematical abilities and analytical skills.
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