Prime Factorization is a mathematical method used 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, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we could simplify equations and fractions, in addition understand the characteristics of that number. Let’s get a closer look.
Ways for Determining Prime Factorization
There are two primary methods for figuring out prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. Both techniques will give you the same result.
Factor Tree Method
The initial way is utilizing 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, make branches for the factors.
Continue making branches and factoring until you reach a prime number.
Here’s an example 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 will be 2 x 2 x 3 x 3. To visualize this procedure, we could create a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is comprehended by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next process for working out the prime factorization of a number is to start using a record of prime numbers. Note the value you are trying to factor. Next, divide the value by a prime number that divides evenly into it. It’s easiest to begin with the initial few prime numbers, like 2, 3, and 5.
Let’s use the division process for prime factorization of 36.
What is a prime number that divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? No.
What is a prime number that divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
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 visualization.
Utilizing both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a few examples, let’s do one more utilizing both processes.
Let’s use 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try the division process:
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 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.
Applications of Prime Factorization
Prime factorization has several real-life utilizations in math. One of the primary applications is simplifying 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 can be simplified by working out 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 streamlined fraction of 1/3.
To see how this functions, let's utilize 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 rule out any 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 executes a crucial role in cryptography and computer science. As you progress in advanced mathematics and science concepts, you will figure out more utilizations for prime factorization and be glad you are an expert.
It’s Prime Time to Enhance Your Math Abilities
Prime factorization is a crucial concept in math which allows us to simplify equations and fractions, moreover understand the properties of a number. By practicing and comprehending the methods and applications of prime factorization, we can improve our mathematical abilities and problem-solving abilities.
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