Prime Factorization is a mathematical function employed to split up 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 figuring out the prime factors of a number, we could simplify fractions and equations, also learn the characteristics of that number. Let’s look closely.
Ways for Determining Prime Factorization
There are two major processes for figuring out prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other processes will give you the same result.
Factor Tree Method
The primary method is using a factor tree. To create a factor tree:
Begin by noting the number you are trying to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring till 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 are done here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To imagine this process, we can make a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next process for figuring out the prime factorization of a number is to start utilizing a record of prime numbers. Note the value you are attempting to factor. Subsequently, divide the number by a prime number that divides evenly into it. It’s easiest to begin with the first few prime numbers, like 2, 3, and 5.
Let’s utilize 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? No.
What is a prime number which 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 chart.
Using both methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked by the means of a some examples, let’s do one more 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 that 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 here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has many realistic uses in math. One of the primary utilizations is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and streamline the fraction.
For example, the fraction 8/24 can be streamlined by working out the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To check how this operates, let's use prime factorization to simplify the fraction 8/24. First, 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 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 executes a crucial part in computer science and cryptography. As you progress in advanced mathematics and science concepts, you will find further uses for prime factorization and be delighted you are a professional.
It’s the Best Time to Enhance Your Mathematical Abilities
Prime factorization is an essential theory in mathematics which enables us to streamline equations and fractions, moreover get a grasp of the characteristics of a number. By practicing and comprehending the processes and applications of prime factorization, we could improve our math skills and problem-solving skills.
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