Prime Factorization is a mathematical method utilized to segregate 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 just be divided by 1 and themselves, for instance 2, 3, 5, and 7.
By working out the prime factors of a number, we can simplify fractions and equations, also understand the properties of that number. Let’s look closely.
Ways for Figuring out Prime Factorization
There are two primary methods for performing prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. Both methods will give you the same result.
Factor Tree Method
The primary way is utilizing a factor tree. To create a factor tree:
Begin by noting the value you are attempting to factor at the top of the page.
Underneath, create branches for the factors.
Continue creating branches and factoring until you reach 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 here.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this process, we could make a factor tree for 36 as follows.
Consequently, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second process for finding the prime factorization of a number is to start utilizing a record of prime numbers. Note down the number you are trying to factor. Then, divide the number by a prime number which divides evenly into it. It’s easiest to begin 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 that 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 visualization.
Utilizing both process, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked through a some examples, let’s do one more utilizing both processes.
Let’s utilize 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 test the division method:
What is the prime factorization for 100?
What is a prime number that 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? No.
What is a prime number which divides into 25? 5 * 5 = 25
Is 5 a prime number? Yes. We are done.
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 primary uses is simplifying fractions. By finding out the prime factorization of the numerator and denominator of a fraction, you could cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 can be streamlined by finding the prime factorization of both numbers. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By canceling 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. Primarily, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Subsequently, we cancel out ever common prime factors between 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 an important role in cryptography and computer science. As you go ahead in progressive math and science theories, you will find more utilizations for prime factorization and be glad you are a professional.
It’s Peak Hour to Boost Your Math Abilities
Prime factorization is a crucial concept in math which enables us to simplify equations and fractions, also understand the properties of a number. By practicing and understanding the processes and utilizations of prime factorization, we can improve our math skills and analytical skills.
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