Prime Factorization is a mathematical method utilized to split up 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, for instance 2, 3, 5, and 7.
By finding the prime factors of a number, we could streamline fractions and equations, as well as understand the characteristics of that number. Let’s look closely.
Methods for Figuring out Prime Factorization
There are two main methods for figuring out prime factorization. You can utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other techniques will give you the same outcome.
Factor Tree Method
The primary method is utilizing a factor tree. To create a factor tree:
Initiate by noting the number you are trying to factor at the top of the page.
Under it, make branches for the factors.
Continue creating branches and factoring before you reach a prime number.
Here’s an instance 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 will be 2 x 2 x 3 x 3. To envision this procedure, we can create a factor tree for 36 as ensues.
Consequently, 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 second process for working out the prime factorization of a number is to start using a list of prime numbers. Write down the value you are attempting to factor. Then, divide the value by a prime number that divides equally into it. It’s most convenient to start with the first few prime numbers, like 2, 3, and 5.
Let’s utilize 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? Nope.
What is a prime number that 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 established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked by the means of a few examples, let’s do another one utilizing both methods.
Let’s utilize 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 clear.
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? 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.
Applications of Prime Factorization
Prime factorization has several realistic uses in math. One of the major 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 simplify the fraction.
For example, the fraction 8/24 can be streamlined by working out the prime factorization of both values. 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 operates, let's use 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
Subsequently, we cancel out any common prime factors among 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 remained with the simplified fraction of 1/3.
Prime factorization also executes a crucial part in cryptography and computer science. As you progress in sophisticated mathematics and science theories, you will figure out further utilizations for prime factorization and be glad you are a pro.
It’s Prime Time to Advance Your Math Skills
Prime factorization is an essential theory in mathematics that enables us to streamline equations and fractions, also learn the properties of a number. By practicing and understanding the methods and uses of prime factorization, we can improve our math abilities and problem-solving skills.
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