Prime Factorization is a mathematical method employed 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 only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can simplify fractions and equations, also understand the properties of that number. Let’s get a closer look.
Ways for Finding Prime Factorization
There are two major processes for working out prime factorization. You could utilize a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will give you the same answer.
Factor Tree Method
The initial way is utilizing a factor tree. To make a factor tree:
Start by noting the value you are trying to factor at the start of the page.
Below it, make branches for the factors.
Proceed by drawing branches and factoring until 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 have reached the end.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To visualize this process, we can create a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for figuring out the prime factorization of a number is to start utilizing a record of prime numbers. Note down the value you are attempting to factor. Then, divide the number by a prime number which divides evenly into it. It’s most convenient to begin 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? No.
What is a prime number that 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 process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve previously worked through a few examples, let’s do one more employing 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 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 that divides into 50? 2 * 25 = 50
Is 25 a prime number? Nope.
What is a prime number that 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.
Applications of Prime Factorization
Prime factorization has multiple realistic applications in math. One of the primary uses is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 can 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 simplified fraction of 1/3.
To see how this works, let's use prime factorization to streamline the fraction 8/24. Primarily, 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 ruling out the common prime factors of 2, we are left with the streamlined fraction of 1/3.
Prime factorization additionally plays an important role in computer science and cryptography. As you progress in sophisticated math and science theories, you will find additional applications for prime factorization and be pleased you are a pro.
It’s the Best Time to Advance Your Math Skills
Prime factorization is a crucial theory in mathematics which allows us to streamline equations and fractions, moreover understand the properties of a value. By practicing and comprehending the methods and utilizations of prime factorization, we could improve our mathematical abilities and problem-solving skills.
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With the assistance of Grade Potential tutoring, you could enhance your mathematical abilities, improve your confidence, and achieve your academic goals.
