Prime Factorization is a mathematical function 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 just be divided by 1 and themselves, for example 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify equations and fractions, in addition understand the properties of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two major processes for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other processes will grant you the same answer.
Factor Tree Method
The first way is using a factor tree. To make a factor tree:
Start by noting the value you are trying to factor at the start of the page.
Under it, 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 know 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 visualize this method, we can make a factor tree for 36 as follows.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for finding the prime factorization of a number is to begin using a list of prime numbers. Note down the value you are attempting to factor. Subsequently, divide the value by a prime number which divides evenly into it. It’s simplest 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? 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.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a visualization.
Utilizing both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve earlier worked through a few examples, let’s do another one utilizing both methods.
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 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? Nope.
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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has multiple real-life applications in math. One of the major utilizations is streamlining 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 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 streamlined fraction of 1/3.
To check how this operates, 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
Next, we rule out ever common prime factors among 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 an important role in cryptography and computer science. As you go ahead in sophisticated mathematics and science studies, you will figure out additional utilizations for prime factorization and be glad you are an expert.
It’s the Best Time to Boost Your Mathematical Abilities
Prime factorization is an important concept in mathematics that enables us to streamline equations and fractions, moreover get a grasp of the properties of a value. By practicing and comprehending the processes and applications of prime factorization, we could improve our math skills and problem-solving abilities.
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With the help of Grade Potential tutoring, you can improve your math abilities, improve your confidence, and reach your academic goals.
