Prime Factorization is a mathematical function used to break down 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 figuring out the prime factors of a number, we can simplify equations and fractions, also understand the properties of that number. Let’s get a closer look.
Processes for Figuring out Prime Factorization
There are two major ways for working out prime factorization. You can use a factor tree, or you could factor by dividing by prime numbers. Both processes will grant you the exact result.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Start by writing the value you are trying to factor at the top of the page.
Underneath, create branches for the factors.
Proceed by drawing branches and factoring before you reach 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this process, we could make a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for finding the prime factorization of a number is to initiate using a list of prime numbers. Note down the number you are attempting to factor. Next, divide the value by a prime number that divides evenly into it. It’s easiest to initiate with the initial 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? 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.
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 earlier worked by the means of a some examples, let’s do another one 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 done here.
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 which 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 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 main utilizations 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 simplified by finding 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 check how this operates, 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
Subsequently, we cancel out any common prime factors among 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 also plays a crucial role in cryptography and computer science. As you proceed in progressive mathematics and science studies, you will figure out additional utilizations for prime factorization and be glad you are an expert.
It’s Prime Time to Enhance Your Math Abilities
Prime factorization is an essential concept in math that allows us to simplify equations and fractions, also get a grasp of the properties of a value. By practicing and understanding the processes and utilizations of prime factorization, we could enhance our mathematical abilities and problem-solving skills.
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