Prime Factorization is a mathematical function employed to break down 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, such as 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can streamline equations and fractions, also understand the characteristics of that number. Let’s get a closer look.
Processes for Figuring out Prime Factorization
There are two main ways 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 yield you the exact outcome.
Factor Tree Method
The initial way is utilizing a factor tree. To create a factor tree:
Start by noting the number you are trying to factor at the start of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring until you reach a prime number.
Here’s an example of the thought process:
We recognize 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 imagine this method, we could create a factor tree for 36 as follows.
As you can see, the prime factorization of 36 is figured out by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for working out the prime factorization of a number is to begin utilizing a list of prime numbers. Note the value you are trying to factor. Then, divide the value by a prime number that divides evenly into it. It’s simplest to initiate with the initial 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? No.
What is a prime number which 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 chart.
Utilizing both systems, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a some examples, let’s do one more employing both methods.
Let’s use a factor tree to work 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 done here.
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? No.
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 multiple real-life utilizations in math. One of the primary utilizations is streamlining fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 can be simplified 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 utilize prime factorization to simplify the fraction 8/24. Primarily, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we rule out ever 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 an important role in cryptography and computer science. As you progress in progressive math and science theories, you will figure out additional utilizations for prime factorization and be glad you are a pro.
It’s Peak Hour to Boost Your Mathematical Abilities
Prime factorization is an essential theory in math which enables us to streamline equations and fractions, as well as learn the properties of a number. By practicing and comprehending the processes and utilizations of prime factorization, we could enhance our math skills and analytical abilities.
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