Prime Factorization is a mathematical method employed to break down a composite number into its prime factors. Composite numbers can be divided by more than just 1 and itself to conclude 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 could streamline equations and fractions, in addition understand the properties of that number. Let’s look closely.
Ways for Determining Prime Factorization
There are two major ways 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 techniques will grant you the same result.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Begin by writing the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring till you arrive at a prime number.
Here’s an example of the thought 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 will be 2 x 2 x 3 x 3. To envision this procedure, we could make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for working out the prime factorization of a number is to start utilizing a record of prime numbers. Note down the number you are trying to factor. Next, divide the value by a prime number which divides equally into it. It’s simplest to begin with the initial 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 which 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 depiction.
Utilizing both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked by the means of a few examples, let’s do one more utilizing both processes.
Let’s use a factor tree to figure 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 here.
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 that divides into 100? 2 * 50 = 100
Is 50 a prime number? No.
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.
Applications of Prime Factorization
Prime factorization has many realistic uses in math. One of the main uses 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 simplify the fraction.
For example, the fraction 8/24 could be streamlined by solving 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 simplified fraction of 1/3.
To see how this functions, 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
Then, we rule 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 simplified fraction of 1/3.
Prime factorization additionally executes a crucial role in cryptography and computer science. As you proceed in advanced math and science concepts, you will figure out further applications for prime factorization and be pleased you are a professional.
It’s Peak Hour to Boost Your Mathematical Abilities
Prime factorization is a crucial concept in math that allows us to streamline equations and fractions, also learn the properties of a number. By practicing and understanding the processes and uses of prime factorization, we can enhance our mathematical skills and problem-solving abilities.
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