Prime Factorization is a mathematical method used to segregate 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 only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we could streamline equations and fractions, in addition learn the properties of that number. Let’s get a closer look.
Processes for Figuring out Prime Factorization
There are two major methods for working out prime factorization. You could employ a factor tree, or you can factor by dividing by prime numbers. Both methods will grant you the same result.
Factor Tree Method
The first method is utilizing a factor tree. To create a factor tree:
Initiate by noting the number you are trying to factor at the start of the page.
Under it, make branches for the factors.
Proceed by making branches and factoring before you attain 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 will be 2 x 2 x 3 x 3. To envision this procedure, we could make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is figured out 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 the value you are trying to factor. Then, divide the value by a prime number that divides evenly into it. It’s easiest to begin with the initial few prime numbers, like 2, 3, and 5.
Let’s use the division process for prime factorization of 36.
What is a prime number which 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? No.
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 chart.
Using both systems, we established 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 some examples, let’s do another one using both methods.
Let’s utilize a factor tree to find 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.
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 which 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? No.
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.
Uses of Prime Factorization
Prime factorization has multiple realistic utilizations in math. One of the main applications 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 simplify the fraction.
For example, the fraction 8/24 could be simplified by solving 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 utilize 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
Next, we rule out any 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 also executes an important part in computer science and cryptography. As you go ahead in progressive mathematics and science theories, you will find further utilizations for prime factorization and be delighted you are an expert.
It’s the Best Time to Boost Your Mathematical Abilities
Prime factorization is a crucial concept in mathematics which allows us to simplify equations and fractions, as well as learn the characteristics of a value. By practicing and understanding the processes and utilizations of prime factorization, we could enhance our math abilities and problem-solving skills.
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