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 only be divided by 1 and themselves, for example 2, 3, 5, and 7.
By figuring out the prime factors of a number, we could simplify fractions and equations, in addition understand the characteristics of that number. Let’s take a closer look.
Ways for Finding Prime Factorization
There are two major ways for working out prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. One as well as the other processes will grant you the exact answer.
Factor Tree Method
The first way is using a factor tree. To make a factor tree:
Begin by noting the value you are attempting to factor at the start of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring before 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 here.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this method, we can create a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for finding the prime factorization of a number is to start using a list of prime numbers. Write down the number you are trying to factor. Subsequently, divide the value by a prime number which divides evenly into it. It’s simplest to initiate 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 which 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? No.
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 depiction.
Using both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve already worked by the means of a few examples, let’s do another one utilizing both methods.
Let’s use 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 clear.
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? No.
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.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has many practical uses in math. One of the major uses is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline 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 ruling 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. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, 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 remained with the simplified fraction of 1/3.
Prime factorization further plays a crucial part in cryptography and computer science. As you proceed in advanced math and science theories, you will find further applications for prime factorization and be delighted you are an expert.
It’s Prime Time to Boost Your Mathematical Skills
Prime factorization is an essential theory in mathematics which allows 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 can improve our mathematical skills and analytical skills.
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