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 example 2, 3, 5, and 7.
By figuring out 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.
Processes for Determining Prime Factorization
There are two primary processes for performing prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. Both techniques will grant you the exact answer.
Factor Tree Method
The initial method is utilizing a factor tree. To create a factor tree:
Begin by writing the number you are attempting to factor at the top of the page.
Underneath, create branches for the factors.
Proceed by creating branches and factoring until you attain a prime number.
Here’s an example of the thinking process:
We recognize 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 envision this procedure, we could make 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 second way for finding the prime factorization of a number is to start using a record of prime numbers. Note down the value you are trying to factor. Next, divide the value by a prime number which divides equally into it. It’s simplest to start with the first few prime numbers, like 2, 3, and 5.
Let’s use the division process for prime factorization of 36.
What is a prime number which divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? Nope.
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 here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both process, we established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve previously worked by the means of a some examples, let’s do one more using both processes.
Let’s utilize 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 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? No.
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.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has many real-life utilizations in mathematics. One of the major uses is streamlining fractions. By finding out 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 working out the prime factorization of both values. 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 works, let's utilize prime factorization to streamline the fraction 8/24. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we rule 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 streamlined fraction of 1/3.
Prime factorization further plays an essential role in cryptography and computer science. As you proceed in advanced mathematics and science concepts, you will figure out additional uses for prime factorization and be glad you are a professional.
It’s Prime Time to Advance Your Math Abilities
Prime factorization is an important theory in math that enables us to simplify equations and fractions, also understand the characteristics of a number. By practicing and comprehending the processes and utilizations of prime factorization, we can improve our mathematical skills and problem-solving skills.
If you need assistance conquering prime factorization, contemplate connect with Grade Potential tutoring for professional support. Grade Potential teachers are skilled and educated in math. They can provide customized instruction and assistance to support you comprehend and apply prime factorization in your studies.
With the assistance of Grade Potential tutoring, you could advance your math abilities, improve your confidence, and attain your academic objectives.
