Prime Factorization is a mathematical function employed to segregate 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 instance 2, 3, 5, and 7.
By figuring out the prime factors of a number, we can streamline equations and fractions, in addition learn the properties of that number. Let’s take a closer look.
Processes for Figuring out Prime Factorization
There are two main processes for performing 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 grant you the same outcome.
Factor Tree Method
The first way is using a factor tree. To create a factor tree:
Begin by writing the number you are attempting to factor at the start of the page.
Under it, create branches for the factors.
Proceed by drawing branches and factoring till you attain 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.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this process, we can create a factor tree for 36 as follows.
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 method for working out the prime factorization of a number is to start using a record of prime numbers. Note down the value you are attempting to factor. Then, divide the value by a prime number which divides equally into it. It’s easiest to begin 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 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 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 chart.
Utilizing both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve already worked through a few examples, let’s do another one utilizing both processes.
Let’s use 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 that 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 multiple real-life utilizations in mathematics. One of the primary 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 clarify the fraction.
For instance, the fraction 8/24 could be simplified by finding 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 clarified fraction of 1/3.
To see how this works, let's employ prime factorization to simplify the fraction 8/24. First, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we cancel 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 streamlined fraction of 1/3.
Prime factorization further plays an important part in cryptography and computer science. As you proceed in sophisticated math and science studies, you will find additional utilizations for prime factorization and be glad you are an expert.
It’s Peak Hour 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 properties of a number. By practicing and comprehending the processes and uses of prime factorization, we can enhance our mathematical abilities and analytical abilities.
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