Prime Factorization is a mathematical function used to split up 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 figuring out the prime factors of a number, we can streamline fractions and equations, also learn the properties of that number. Let’s look closely.
Processes for Finding Prime Factorization
There are two primary methods for working out prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both techniques will grant you the exact outcome.
Factor Tree Method
The first method is using a factor tree. To make a factor tree:
Initiate by writing the value you are trying to factor at the top of the page.
Underneath, create branches for the factors.
Proceed by making 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 are done here.
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 figured out by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for figuring out the prime factorization of a number is to initiate using a list of prime numbers. Write down the value you are trying to factor. Next, divide the number by a prime number which divides equally into it. It’s most convenient to begin with the initial few prime numbers, like 2, 3, and 5.
Let’s utilize 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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both process, 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 another one using both methods.
Let’s utilize a factor tree to figure out the prime factorization of 100.
We learned 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 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 that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
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.
Utilizations of Prime Factorization
Prime factorization has many practical utilizations in mathematics. One of the major utilizations is simplifying fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and simplify the fraction.
For example, the fraction 8/24 could be streamlined by solving the prime factorization of both numbers. 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 operates, let's utilize prime factorization to simplify the fraction 8/24. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we cancel out any common prime factors between 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 important role in cryptography and computer science. As you go ahead in sophisticated mathematics and science studies, you will find additional applications for prime factorization and be pleased you are an expert.
It’s Prime Time to Enhance Your Math Abilities
Prime factorization is an important theory in math which enables us to streamline equations and fractions, moreover get a grasp of the properties of a number. By practicing and understanding the methods and uses of prime factorization, we can improve our math skills and problem-solving abilities.
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With the assistance of Grade Potential tutoring, you could enhance your mathematical abilities, improve your confidence, and reach your academic aims.
