Prime Factorization is a mathematical method 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 example 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can simplify equations and fractions, also learn the properties of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two main methods for performing prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both processes will give you the exact outcome.
Factor Tree Method
The first way is using a factor tree. To make a factor tree:
Start by noting the number you are attempting to factor at the start of the page.
Below it, create branches for the factors.
Proceed by creating branches and factoring till you attain a prime number.
Here’s an example of the thought 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 can make a factor tree for 36 as ensues.
Consequently, 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 second way for figuring out the prime factorization of a number is to start using a record of prime numbers. Note down the value you are trying to factor. Subsequently, divide the number by a prime number that divides evenly into it. It’s easiest to start 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 which divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? No.
What is a prime number which 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 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 few examples, let’s do another one employing both methods.
Let’s use a factor tree to find 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 clear.
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 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.
Uses of Prime Factorization
Prime factorization has multiple real-life applications in math. One of the main uses is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify 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 canceling out the common prime factor of 2, we are left with the clarified fraction of 1/3.
To check how this works, 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
Next, we rule out ever 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 left with the simplified fraction of 1/3.
Prime factorization further executes a crucial part in computer science and cryptography. As you progress in sophisticated math and science studies, you will find additional utilizations for prime factorization and be delighted you are a professional.
It’s Prime Time to Enhance Your Math Skills
Prime factorization is an important concept in mathematics which allows us to simplify equations and fractions, as well as understand the characteristics of a value. By practicing and understanding the methods and uses of prime factorization, we could enhance our math abilities and analytical abilities.
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