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 conclude in a whole number. Prime numbers can only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we can simplify fractions and equations, in addition understand the characteristics of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two main processes for working out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. Both methods will grant you the same outcome.
Factor Tree Method
The primary method is utilizing a factor tree. To make a factor tree:
Initiate by writing the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Continue making branches and factoring till you reach a prime number.
Here’s an instance of the thinking process:
We know 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 will be 2 x 2 x 3 x 3. To imagine this process, we can make 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, that is 2 * 3 * 2 * 3.
Division Method
The second process for finding the prime factorization of a number is to initiate utilizing a record of prime numbers. Write down the value you are attempting to factor. Subsequently, divide the number by a prime number which divides evenly into it. It’s most convenient to initiate with the initial 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 which 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a visualization.
Using both process, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked through a few examples, let’s do another one utilizing both processes.
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 done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s test 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? Nope.
What is a prime number which 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 several realistic applications in mathematics. 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 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 clarified fraction of 1/3.
To check how this functions, let's employ prime factorization to streamline the fraction 8/24. First, work on 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 ruling out the common prime factors of 2, we are left with the simplified fraction of 1/3.
Prime factorization additionally plays a crucial role in cryptography and computer science. As you progress in progressive mathematics and science studies, you will figure out additional applications for prime factorization and be delighted you are a pro.
It’s the Best Time to Advance Your Mathematical Skills
Prime factorization is a crucial concept in mathematics which enables us to simplify equations and fractions, moreover get a grasp of the characteristics of a value. By practicing and comprehending the processes and utilizations of prime factorization, we could improve our mathematical abilities and problem-solving skills.
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With the support of Grade Potential tutoring, you could enhance your math skills, boost your confidence, and attain your academic aims.
