Prime Factorization is a mathematical function employed to segregate 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 example 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can simplify equations and fractions, also understand the characteristics of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two major processes for performing prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both techniques will give you the exact result.
Factor Tree Method
The primary method is utilizing a factor tree. To make a factor tree:
Begin by writing the value you are attempting to factor at the top of the page.
Under it, make branches for the factors.
Continue drawing branches and factoring till you reach a prime number.
Here’s an example of the thought 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 process, we could create a factor tree for 36 as follows.
As demonstrated, 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 working out the prime factorization of a number is to begin utilizing a record of prime numbers. Note down the number you are attempting to factor. Subsequently, divide the value by a prime number that divides evenly into it. It’s most convenient 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 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.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing 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 earlier worked by the means of a few examples, let’s do another one utilizing both methods.
Let’s utilize 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 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? No.
What is a prime number which 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.
Utilizations of Prime Factorization
Prime factorization has many real-life uses in math. One of the main uses 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 streamlined by finding the prime factorization of both numbers. 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 operates, let's use prime factorization to streamline the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we rule out any common prime factors among the numerator and denominator.
8/24 = 2 * 2 * 2 / 2 * 2 * 2 * 3 = 1/3
After canceling out the common prime factors of 2, we are remained with the streamlined fraction of 1/3.
Prime factorization also executes an essential part in cryptography and computer science. As you proceed in advanced math and science theories, you will find additional utilizations for prime factorization and be delighted you are a pro.
It’s Peak Hour to Advance Your Mathematical Skills
Prime factorization is a crucial theory in math that allows us to simplify equations and fractions, moreover get a grasp of the characteristics of a value. By practicing and comprehending the processes and utilizations of prime factorization, we could enhance our math abilities and analytical skills.
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