Prime Factorization is a mathematical function utilized 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, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify fractions and equations, also understand the characteristics of that number. Let’s take a closer look.
Processes for Finding Prime Factorization
There are two major ways for figuring out prime factorization. You can use a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will yield you the same outcome.
Factor Tree Method
The first 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.
Below it, make branches for the factors.
Continue creating branches and factoring before you attain a prime number.
Here’s an instance of the thinking process:
We know 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 create a factor tree for 36 as follows.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for finding the prime factorization of a number is to begin using a list of prime numbers. Note down the value you are trying to factor. Next, divide the number by a prime number which divides evenly into it. It’s simplest 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 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? 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 depiction.
Utilizing both process, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve earlier worked by the means of a few examples, let’s do another one using both methods.
Let’s utilize a factor tree to find 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 done.
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? 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.
Utilizations of Prime Factorization
Prime factorization has several practical applications in math. One of the primary utilizations is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline the fraction.
For instance, the fraction 8/24 could 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 clarified fraction of 1/3.
To see how this functions, let's employ prime factorization to streamline the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, 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 remained with the simplified fraction of 1/3.
Prime factorization further plays an important part in computer science and cryptography. As you go ahead in sophisticated mathematics and science theories, you will figure out additional applications for prime factorization and be delighted you are a professional.
It’s the Best Time to Advance Your Math Skills
Prime factorization is a crucial theory in math that allows us to streamline equations and fractions, as well as understand the properties of a value. By practicing and understanding the methods and applications of prime factorization, we could improve our mathematical abilities and analytical skills.
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