Prime Factorization is a mathematical method employed to segregate 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 just be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify equations and fractions, in addition understand the properties of that number. Let’s look closely.
Methods for Figuring out Prime Factorization
There are two primary ways for performing prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other processes will yield you the exact outcome.
Factor Tree Method
The initial method is utilizing a factor tree. To create a factor tree:
Begin by noting the value you are trying to factor at the start of the page.
Below it, make branches for the factors.
Proceed by creating branches and factoring till you attain 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 have reached the end.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To visualize this procedure, we can make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second method for figuring out the prime factorization of a number is to start using a list of prime numbers. Note the number you are attempting to factor. Next, divide the value by a prime number which divides evenly into it. It’s most convenient to start 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 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 chart.
Using both methods, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve already worked by the means of a some examples, let’s do another one employing both processes.
Let’s utilize 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 done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try 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? Nope.
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 many real-life uses in mathematics. One of the major 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 simplify the fraction.
For example, the fraction 8/24 could be streamlined 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 simplified fraction of 1/3.
To see how this operates, let's utilize 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
Then, we rule out ever common prime factors between 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 left with the simplified fraction of 1/3.
Prime factorization also plays an important part in computer science and cryptography. As you proceed in advanced mathematics and science concepts, you will find additional uses for prime factorization and be pleased you are an expert.
It’s Prime Time to Advance Your Mathematical Skills
Prime factorization is a crucial concept in math which allows us to streamline equations and fractions, moreover learn the properties of a number. By practicing and understanding the processes and utilizations of prime factorization, we could improve our math abilities and problem-solving abilities.
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