Prime Factorization is a mathematical function used to split up a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can just be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can streamline equations and fractions, also learn the properties of that number. Let’s take a closer look.
Ways for Finding Prime Factorization
There are two major ways for performing prime factorization. You could employ a factor tree, or you can factor by dividing by prime numbers. One as well as the other processes will grant you the same outcome.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Initiate by noting the value you are trying to factor at the top of the page.
Below it, create branches for the factors.
Proceed by creating branches and factoring until you arrive at 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 will be 2 x 2 x 3 x 3. To imagine this procedure, we could make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next process for finding the prime factorization of a number is to begin utilizing a record of prime numbers. Note the number you are attempting to factor. Then, divide the number by a prime number that divides evenly into it. It’s simplest 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 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? Nope.
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 visualization.
Utilizing both systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked through a few examples, let’s do one more using both processes.
Let’s utilize a factor tree to figure 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.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s test 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? Nope.
What is a prime number which divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
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 many real-life utilizations in math. One of the main utilizations 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 instance, the fraction 8/24 can be simplified by solving the prime factorization of both values. 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 check how this works, let's utilize 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 cancel out ever common prime factors within 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 remained with the streamlined fraction of 1/3.
Prime factorization also executes an essential part in cryptography and computer science. As you proceed in progressive mathematics and science studies, you will figure out more uses for prime factorization and be glad you are a pro.
It’s Prime Time to Enhance Your Mathematical Abilities
Prime factorization is an important theory in mathematics that allows us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and comprehending the methods and uses of prime factorization, we could improve our math abilities and analytical skills.
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