Prime Factorization is a mathematical function utilized 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 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, as well as understand the characteristics of that number. Let’s look closely.
Ways for Figuring out Prime Factorization
There are two major methods for performing prime factorization. You could use a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will yield you the exact outcome.
Factor Tree Method
The primary method is using a factor tree. To make a factor tree:
Begin by noting the number you are trying to factor at the top of the page.
Under it, create branches for the factors.
Proceed by drawing branches and factoring till you attain a prime number.
Here’s an instance 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 would be 2 x 2 x 3 x 3. To visualize this procedure, we can create a factor tree for 36 as follows.
As demonstrated, 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 figuring out the prime factorization of a number is to initiate using a record of prime numbers. Note the value you are trying to factor. Next, divide the number by a prime number that divides equally 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? No.
What is a prime number that 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.
Using both process, 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 few examples, let’s do one more employing both processes.
Let’s use a factor tree to work 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.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try 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? No.
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.
Uses of Prime Factorization
Prime factorization has many real-life applications in math. One of the main uses 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 simplify the fraction.
For example, the fraction 8/24 could be streamlined by solving 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 use 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 cancel out ever 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 further plays an important part in computer science and cryptography. As you progress in advanced mathematics and science concepts, you will find more applications for prime factorization and be delighted you are an expert.
It’s the Best Time to Advance Your Math Abilities
Prime factorization is a crucial concept in math which allows us to simplify equations and fractions, as well as understand the characteristics of a number. By practicing and comprehending the processes and applications of prime factorization, we can enhance our mathematical skills and analytical skills.
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With the assistance of Grade Potential tutoring, you can improve your mathematical abilities, improve your confidence, and reach your academic goals.
