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 result in a whole number. Prime numbers can just be divided by 1 and themselves, such as 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can streamline fractions and equations, also understand the characteristics of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two primary methods for performing prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will yield you the same answer.
Factor Tree Method
The first method is using a factor tree. To create a factor tree:
Start by noting the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Continue drawing 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 have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this process, we could create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second method for figuring out the prime factorization of a number is to start utilizing a list of prime numbers. Write down the value you are attempting to factor. Next, divide the value by a prime number which divides evenly into it. It’s simplest to start with the initial few prime numbers, like 2, 3, and 5.
Let’s utilize 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 chart.
Utilizing both methods, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked through a few examples, let’s do another one utilizing both processes.
Let’s utilize a factor tree to find 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 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 that divides into 50? 2 * 25 = 50
Is 25 a prime number? Nope.
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 utilizations in math. One of the primary utilizations is simplifying 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 instance, the fraction 8/24 could be streamlined 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 streamlined fraction of 1/3.
To check how this works, let's employ prime factorization to simplify the fraction 8/24. Primarily, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel 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 further executes a crucial part in computer science and cryptography. As you proceed in progressive mathematics and science concepts, you will figure out more utilizations for prime factorization and be pleased you are a professional.
It’s the Best Time to Advance Your Math Abilities
Prime factorization is a crucial concept in mathematics which enables us to streamline equations and fractions, as well as get a grasp of the characteristics of a value. By practicing and comprehending the methods and uses of prime factorization, we could improve our mathematical abilities and analytical abilities.
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With the support of Grade Potential tutoring, you could advance your mathematical skills, boost your confidence, and attain your academic objectives.
