Prime Factorization is a mathematical method utilized 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 can streamline equations and fractions, in addition learn the characteristics of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two main processes 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 yield you the exact outcome.
Factor Tree Method
The primary way is using a factor tree. To create a factor tree:
Begin by noting the value you are trying to factor at the start of the page.
Below it, create branches for the factors.
Continue making branches and factoring till you attain a prime number.
Here’s an instance 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 are done.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this method, we can create 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 next method for finding the prime factorization of a number is to initiate utilizing a list of prime numbers. Note the value you are attempting to factor. Then, divide the value by a prime number which divides evenly into it. It’s easiest to initiate with the first 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? 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 chart.
Using both methods, 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 another one employing both processes.
Let’s utilize a factor tree to work 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 process:
What is the prime factorization for 100?
What is a prime number that divides into 100? 2 * 50 = 100
Is 50 a prime number? Nope.
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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has multiple realistic 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 simplify the fraction.
For example, the fraction 8/24 could be simplified by working out 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 streamlined fraction of 1/3.
To see how this operates, let's use 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
Then, we rule out ever common prime factors among 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 left with the simplified fraction of 1/3.
Prime factorization additionally plays an important role in computer science and cryptography. As you progress in advanced mathematics and science theories, you will find further utilizations for prime factorization and be delighted you are a professional.
It’s Peak Hour to Boost Your Mathematical Abilities
Prime factorization is a crucial theory in mathematics which allows us to streamline equations and fractions, also get a grasp of the characteristics of a number. By practicing and comprehending the methods and uses of prime factorization, we could improve our mathematical abilities and analytical abilities.
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