Prime Factorization is a mathematical function employed to segregate a composite number into its prime factors. Composite numbers could 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, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we can streamline fractions and equations, also learn the properties of that number. Let’s take a closer look.
Ways for Figuring out Prime Factorization
There are two main methods for working out prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other techniques will grant you the same result.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Begin by noting the number you are trying to factor at the start of the page.
Under it, make branches for the factors.
Continue drawing branches and factoring before you reach a prime number.
Here’s an example of the thinking process:
We recognize 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 would be 2 x 2 x 3 x 3. To imagine this procedure, we can make a factor tree for 36 as ensues.
As you can see, 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 next process 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. Next, divide the number by a prime number that divides evenly into it. It’s easiest to start 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 which 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 systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve previously worked through a some examples, let’s do one more employing both processes.
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 which 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 done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has several practical applications in math. One of the major applications 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 simplify the fraction.
For instance, 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 ruling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To see how this works, let's use 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 rule out ever common prime factors between 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 also plays an important role in cryptography and computer science. As you go ahead in sophisticated math and science theories, you will find additional uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Advance Your Math Abilities
Prime factorization is a crucial theory in math which allows us to simplify equations and fractions, as well as understand the properties of a number. By practicing and comprehending the processes and uses of prime factorization, we can improve our math abilities and analytical skills.
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