Prime Factorization is a mathematical function employed to segregate 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 instance 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify fractions and equations, as well as understand the characteristics of that number. Let’s look closely.
Methods for Finding Prime Factorization
There are two major methods for figuring out 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 give you the same answer.
Factor Tree Method
The first method is utilizing a factor tree. To make a factor tree:
Start by noting the value you are attempting to factor at the start of the page.
Underneath, create branches for the factors.
Proceed by drawing branches and factoring before you attain 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To envision this method, we could make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for figuring out the prime factorization of a number is to start using a list of prime numbers. Write down the value you are attempting to factor. Next, divide the value by a prime number that divides evenly into it. It’s easiest to start with the initial few prime numbers, like 2, 3, and 5.
Let’s use 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? 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 process, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked through a few examples, let’s do one more employing both processes.
Let’s utilize a factor tree to work out 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 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 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.
Applications of Prime Factorization
Prime factorization has multiple realistic applications in math. One of the major utilizations is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 could be streamlined by working out 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 streamlined fraction of 1/3.
To check how this functions, 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
Subsequently, we cancel out any common prime factors within 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 left with the simplified fraction of 1/3.
Prime factorization additionally executes an important part in cryptography and computer science. As you progress in progressive math and science concepts, you will find further applications for prime factorization and be glad you are a professional.
It’s Peak Hour to Enhance Your Mathematical Skills
Prime factorization is an essential theory in mathematics that enables us to simplify equations and fractions, also get a grasp of the properties of a value. By practicing and understanding the processes and utilizations of prime factorization, we could enhance our math abilities and analytical abilities.
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