Prime Factorization is a mathematical function utilized 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 could simplify fractions and equations, also understand the characteristics of that number. Let’s look closely.
Ways for Figuring out Prime Factorization
There are two major ways for performing prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will give you the same outcome.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Initiate by noting the number you are attempting to factor at the top of the page.
Below it, create branches for the factors.
Continue creating branches and factoring till you arrive at a prime number.
Here’s an example of the thought process:
We understand 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 would be 2 x 2 x 3 x 3. To imagine this method, 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 in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next way for finding the prime factorization of a number is to initiate using a list of prime numbers. Note the number you are trying to factor. Subsequently, divide the value by a prime number that divides evenly into it. It’s simplest to begin 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? No.
What is a prime number which 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 worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked by the means of a some examples, let’s do one more utilizing both processes.
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 done.
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.
Uses of Prime Factorization
Prime factorization has many real-life utilizations in math. One of the main uses 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 example, the fraction 8/24 can be simplified by solving 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 clarified fraction of 1/3.
To check how this operates, let's utilize prime factorization to streamline the fraction 8/24. Primarily, 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 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 streamlined fraction of 1/3.
Prime factorization also executes an important part in cryptography and computer science. As you proceed in progressive mathematics and science studies, you will figure out further uses for prime factorization and be glad you are an expert.
It’s Peak Hour to Advance Your Mathematical Abilities
Prime factorization is an essential theory in math that allows us to simplify equations and fractions, also learn the characteristics of a number. By practicing and comprehending the methods and uses of prime factorization, we could enhance our mathematical abilities and analytical skills.
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