Prime Factorization is a mathematical method utilized to break down a composite number into its prime factors. Composite numbers could 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 figuring out the prime factors of a number, we can streamline equations and fractions, in addition understand the properties of that number. Let’s get a closer look.
Ways for Figuring out Prime Factorization
There are two major processes for working out prime factorization. You can employ a factor tree, or you can factor by dividing by prime numbers. Both methods will grant you the exact outcome.
Factor Tree Method
The primary method is using a factor tree. To make a factor tree:
Initiate by writing the value you are trying to factor at the start of the page.
Underneath, create branches for the factors.
Proceed by drawing branches and factoring until you arrive at a prime number.
Here’s an example 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.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this procedure, we could make a factor tree for 36 as follows.
As you can see, 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 second process for working out the prime factorization of a number is to begin using a record of prime numbers. Write down the number you are trying to factor. Next, divide the value by a prime number that divides equally into it. It’s simplest to initiate 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 that 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 systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve previously worked by the means of a few examples, let’s do one more employing both processes.
Let’s use 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 done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s test the division method:
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 which divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number which 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.
Utilizations of Prime Factorization
Prime factorization has several practical utilizations in mathematics. One of the main applications is streamlining 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 simplified by solving the prime factorization of both values. 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 functions, let's use prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel 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 streamlined fraction of 1/3.
Prime factorization additionally executes an essential role in computer science and cryptography. As you progress in progressive math and science concepts, you will figure out further uses for prime factorization and be glad you are an expert.
It’s the Best Time to Advance Your Math Abilities
Prime factorization is an essential theory in math which allows us to streamline equations and fractions, moreover get a grasp of the properties of a value. By practicing and comprehending the methods and utilizations of prime factorization, we can enhance our math abilities and problem-solving skills.
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With the help of Grade Potential tutoring, you could enhance your mathematical abilities, improve your confidence, and attain your academic objectives.
