Prime Factorization is a mathematical method used to segregate a composite number into its prime factors. Composite numbers can 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 simplify equations and fractions, also understand the characteristics of that number. Let’s look closely.
Processes for Figuring out Prime Factorization
There are two primary ways for performing prime factorization. You can utilize a factor tree, or you could factor by dividing by prime numbers. Both methods will give you the exact answer.
Factor Tree Method
The primary way is utilizing a factor tree. To create a factor tree:
Start by writing the number you are attempting to factor at the start of the page.
Below it, 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 understand 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 create a factor tree for 36 as follows.
Consequently, 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 next method for finding the prime factorization of a number is to begin utilizing a record of prime numbers. Note down the value you are trying to factor. Next, divide the number by a prime number that divides equally into it. It’s easiest to initiate with the initial few prime numbers, like 2, 3, and 5.
Let’s use 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 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 established the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve already worked through a few examples, let’s do another one using both processes.
Let’s utilize 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 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 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 clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has multiple realistic utilizations in mathematics. One of the primary applications is simplifying fractions. By working out 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 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 simplified fraction of 1/3.
To see how this works, let's utilize prime factorization to streamline the fraction 8/24. Foremost, 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 within 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 simplified fraction of 1/3.
Prime factorization additionally plays a crucial role in computer science and cryptography. As you progress in progressive mathematics and science theories, you will figure out additional uses for prime factorization and be delighted you are an expert.
It’s Peak Hour to Enhance Your Math Skills
Prime factorization is a crucial concept in mathematics which enables us to simplify equations and fractions, moreover get a grasp of the characteristics of a number. By practicing and comprehending the processes and uses of prime factorization, we could enhance our math abilities and problem-solving skills.
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With the assistance of Grade Potential tutoring, you could enhance your mathematical skills, boost your confidence, and achieve your academic goals.
