Prime Factorization is a mathematical method used to segregate a composite number into its prime factors. Composite numbers can 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 figuring out the prime factors of a number, we can streamline equations and fractions, as well as understand the characteristics of that number. Let’s get a closer look.
Processes for Figuring out Prime Factorization
There are two main processes for figuring out prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will yield you the exact outcome.
Factor Tree Method
The first method is using a factor tree. To create a factor tree:
Begin by noting the value you are attempting to factor at the top of the page.
Underneath, create branches for the factors.
Proceed by drawing branches and factoring till you reach a prime number.
Here’s an instance 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this process, we could make a factor tree for 36 as ensues.
Consequently, 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 working out the prime factorization of a number is to start utilizing a list of prime numbers. Note the number you are trying to factor. Next, divide the number by a prime number which divides equally into it. It’s most convenient 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 which 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 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 visualization.
Using both systems, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked by the means of a few examples, let’s do one more utilizing both methods.
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 clear.
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 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.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has several real-life uses in math. One of the major 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 clarify the fraction.
For example, the fraction 8/24 could be simplified by finding 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 simplified fraction of 1/3.
To check how this operates, let's utilize prime factorization to simplify the fraction 8/24. Foremost, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we rule out ever common prime factors between 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 simplified fraction of 1/3.
Prime factorization additionally plays an essential part in cryptography and computer science. As you progress in progressive math and science studies, you will figure out more utilizations for prime factorization and be pleased you are a professional.
It’s Peak Hour to Boost Your Math Abilities
Prime factorization is a crucial concept in math that allows us to streamline equations and fractions, as well as understand the characteristics of a value. By practicing and comprehending the processes and utilizations of prime factorization, we could improve our mathematical skills and problem-solving abilities.
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