Prime Factorization is a mathematical function employed to split up a composite number into its prime factors. Composite numbers could 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 finding the prime factors of a number, we can streamline fractions and equations, as well as understand the characteristics of that number. Let’s get a closer look.
Methods for Determining Prime Factorization
There are two primary methods for performing prime factorization. You could use a factor tree, or you could factor by dividing by prime numbers. One as well as the other processes will grant you the same answer.
Factor Tree Method
The primary way is utilizing a factor tree. To create a factor tree:
Initiate by noting the value you are trying to factor at the start of the page.
Below it, make branches for the factors.
Continue creating branches and factoring till you arrive at a prime number.
Here’s an example of the thought 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.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To envision this procedure, we can make a factor tree for 36 as ensues.
Consequently, 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 finding the prime factorization of a number is to begin using a record of prime numbers. Note down the value you are trying to factor. Then, divide the value by a prime number that divides evenly into it. It’s simplest to initiate 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 which 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 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 chart.
Utilizing both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked through a some examples, let’s do another one utilizing both methods.
Let’s use a factor tree to find 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 which 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.
Uses of Prime Factorization
Prime factorization has several real-life uses in mathematics. One of the major applications is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For instance, the fraction 8/24 could be simplified by finding 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 works, 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
Then, we cancel out any common prime factors among 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 additionally executes an important part in cryptography and computer science. As you go ahead in progressive math and science concepts, you will figure out further uses for prime factorization and be pleased you are a pro.
It’s Peak Hour to Advance Your Mathematical Abilities
Prime factorization is a crucial theory in mathematics which allows us to simplify equations and fractions, also get a grasp of the properties of a value. By practicing and comprehending the processes and applications of prime factorization, we can enhance our mathematical skills and analytical skills.
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