Prime Factorization is a mathematical function 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 just be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could streamline fractions and equations, as well as understand the characteristics of that number. Let’s get a closer look.
Ways for Determining Prime Factorization
There are two main ways for figuring out prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will grant you the exact answer.
Factor Tree Method
The primary way is using a factor tree. To make a factor tree:
Start by noting the number you are attempting to factor at the top of the page.
Under it, make branches for the factors.
Continue creating branches and factoring until you attain 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 have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this process, we could create a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next method for finding the prime factorization of a number is to initiate using a record of prime numbers. Note the number you are trying to factor. Subsequently, divide the number by a prime number that divides evenly into it. It’s most convenient to begin 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 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? Nope.
What is a prime number that 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 depiction.
Utilizing both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve earlier worked by the means of a some examples, let’s do one more using both methods.
Let’s use 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 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 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.
Uses of Prime Factorization
Prime factorization has several practical uses in mathematics. One of the main utilizations is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For example, 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 canceling out the common prime factor of 2, we are left with the streamlined fraction of 1/3.
To check how this functions, let's utilize prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out any common prime factors within 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 a crucial role in computer science and cryptography. As you proceed in advanced math and science concepts, you will find more applications for prime factorization and be glad you are a professional.
It’s Peak Hour to Advance Your Math Abilities
Prime factorization is an important theory in math which enables us to simplify equations and fractions, moreover get a grasp of the characteristics of a number. By practicing and comprehending the processes and utilizations of prime factorization, we can improve our mathematical skills and analytical skills.
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With the assistance of Grade Potential tutoring, you could improve your mathematical abilities, improve your confidence, and achieve your academic objectives.
