Prime Factorization is a mathematical method used to break down a composite number into its prime factors. Composite numbers can 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, for example 2, 3, 5, and 7.
By finding the prime factors of a number, we could simplify fractions and equations, in addition learn the properties of that number. Let’s look closely.
Processes for Figuring out Prime Factorization
There are two main processes 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 methods will give you the exact outcome.
Factor Tree Method
The primary method is utilizing a factor tree. To make a factor tree:
Initiate by noting the value you are trying to factor at the top of the page.
Under it, make branches for the factors.
Proceed by drawing branches and factoring till you reach a prime number.
Here’s an instance of the thinking process:
We understand 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 process, we can make 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 method for finding the prime factorization of a number is to initiate utilizing a list of prime numbers. Note the value you are attempting to factor. Then, divide the number by a prime number which divides equally into it. It’s easiest to initiate with the first few prime numbers, like 2, 3, and 5.
Let’s utilize 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? No.
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.
Utilizing both systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked through a some 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 process:
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 which 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.
Applications of Prime Factorization
Prime factorization has multiple practical utilizations in math. One of the major uses is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For instance, the fraction 8/24 can be simplified by finding 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 clarified fraction of 1/3.
To see how this operates, let's use prime factorization to streamline the fraction 8/24. Primarily, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out ever 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 simplified fraction of 1/3.
Prime factorization further plays an essential part in computer science and cryptography. As you go ahead in advanced math and science theories, you will figure out more utilizations for prime factorization and be delighted you are a professional.
It’s Prime Time to Boost Your Math Abilities
Prime factorization is an essential theory in math which enables us to simplify equations and fractions, moreover learn the characteristics of a value. By practicing and understanding the processes and uses of prime factorization, we could enhance our math abilities and problem-solving abilities.
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