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 only be divided by 1 and themselves, for example 2, 3, 5, and 7.
By finding the prime factors of a number, we can streamline fractions and equations, in addition learn the properties of that number. Let’s take a closer look.
Methods for Determining Prime Factorization
There are two primary ways for performing prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. Both processes will yield you the same answer.
Factor Tree Method
The first method is utilizing a factor tree. To make a factor tree:
Begin by writing the value you are trying to factor at the start of the page.
Underneath, make branches for the factors.
Continue making branches and factoring until you reach a prime number.
Here’s an instance of the thought 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 will be 2 x 2 x 3 x 3. To imagine this procedure, we could make a factor tree for 36 as ensues.
Consequently, 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 working out the prime factorization of a number is to start utilizing a list of prime numbers. Write down the number you are attempting to factor. Next, divide the value by a prime number which divides evenly into it. It’s simplest to start 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 which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
What is a prime number that 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.
Utilizing both methods, we found 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 one more utilizing both methods.
Let’s use a factor tree to work 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 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? No.
What is a prime number which divides into 50? 2 * 25 = 50
Is 25 a prime number? Nope.
What is a prime number which divides into 25? 5 * 5 = 25
Is 5 a prime number? Yes. We are clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has several realistic utilizations in mathematics. One of the primary uses is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 could be simplified by solving 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 check how this works, let's utilize prime factorization to streamline the fraction 8/24. Foremost, work on 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 left with the streamlined fraction of 1/3.
Prime factorization also executes an important role in computer science and cryptography. As you proceed in advanced mathematics and science studies, you will find further applications for prime factorization and be delighted you are a pro.
It’s Peak Hour to Advance Your Mathematical Abilities
Prime factorization is an important concept in mathematics that enables us to streamline equations and fractions, as well as learn the properties of a number. By practicing and understanding the processes and uses of prime factorization, we could enhance our mathematical abilities and problem-solving skills.
If you need help mastering prime factorization, contemplate contacting with Grade Potential tutoring for professional assistance. Grade Potential instructors are experienced and knowledgeable in math. They could provide personalized learning and support to help you learn and utilize prime factorization in your studies.
With the support of Grade Potential tutoring, you can enhance your mathematical abilities, improve your confidence, and achieve your academic goals.
