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 conclude in a whole number. Prime numbers can only 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 fractions and equations, also understand the properties of that number. Let’s take a closer look.
Methods for Determining Prime Factorization
There are two main methods for performing prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will grant you the exact answer.
Factor Tree Method
The first method is utilizing a factor tree. To make a factor tree:
Begin by noting the number 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 instance 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 have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this process, we could create a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors in the end of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for working out the prime factorization of a number is to initiate using a record of prime numbers. Write down the number you are attempting to factor. Next, divide the value by a prime number that divides evenly into it. It’s simplest to begin 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 which divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? Nope.
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 established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that 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 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.
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 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? Nope.
What is a prime number that 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.
Uses of Prime Factorization
Prime factorization has many real-life applications in math. One of the primary uses is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 can be simplified by working out 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 works, let's employ prime factorization to simplify the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out any 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 simplified fraction of 1/3.
Prime factorization further executes an essential part in cryptography and computer science. As you proceed in sophisticated math and science concepts, you will find more uses for prime factorization and be glad you are an expert.
It’s Prime Time to Boost Your Math Skills
Prime factorization is a crucial theory in mathematics which enables us to simplify equations and fractions, moreover understand the characteristics of a value. By practicing and comprehending the methods and utilizations of prime factorization, we can improve our math abilities and problem-solving skills.
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