Prime Factorization is a mathematical function 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 only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify fractions and equations, in addition understand the characteristics of that number. Let’s get a closer look.
Ways for Figuring out Prime Factorization
There are two major ways for working out prime factorization. You could employ a factor tree, or you can factor by dividing by prime numbers. Both techniques will give you the same answer.
Factor Tree Method
The primary way is using a factor tree. To create a factor tree:
Start by noting the number you are trying to factor at the start of the page.
Underneath, create branches for the factors.
Continue making branches and factoring before you reach a prime number.
Here’s an instance of the thinking process:
We know 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 imagine this process, we could make a factor tree for 36 as ensues.
Consequently, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, that is 2 * 3 * 2 * 3.
Division Method
The second method for finding the prime factorization of a number is to initiate utilizing a record of prime numbers. Write down the number you are attempting to factor. Then, divide the number by a prime number which divides evenly into it. It’s most convenient to initiate 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 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 chart.
Utilizing both methods, we worked out the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Even though we’ve previously worked by the means of a some examples, let’s do one more using both methods.
Let’s utilize a factor tree to work out the prime factorization of 100.
We learned 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 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 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 done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Utilizations of Prime Factorization
Prime factorization has many realistic applications in mathematics. One of the primary utilizations is simplifying fractions. By finding 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 canceling 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 simplify the fraction 8/24. Primarily, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we rule 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 streamlined fraction of 1/3.
Prime factorization further plays an essential part in computer science and cryptography. As you go ahead in advanced math and science studies, you will find more utilizations for prime factorization and be glad you are a pro.
It’s the Best Time to Enhance Your Math Skills
Prime factorization is an essential theory in math which allows us to simplify equations and fractions, moreover get a grasp of the properties of a number. By practicing and comprehending the processes and uses of prime factorization, we can enhance our mathematical skills and problem-solving abilities.
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