Prime Factorization is a mathematical method used to split up 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, such as 2, 3, 5, and 7.
By working out the prime factors of a number, we could simplify fractions and equations, in addition learn the characteristics of that number. Let’s take a closer look.
Methods for Finding Prime Factorization
There are two main ways for working out prime factorization. You could utilize a factor tree, or you could factor by dividing by prime numbers. Both processes will grant you the exact answer.
Factor Tree Method
The initial method is using a factor tree. To make a factor tree:
Begin by noting the number you are attempting to factor at the start of the page.
Underneath, make branches for the factors.
Continue making branches and factoring before you arrive at 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 here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To visualize this procedure, we can 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, which are 2 * 3 * 2 * 3.
Division Method
The second way for finding the prime factorization of a number is to start utilizing a list of prime numbers. Note down the number you are trying to factor. Next, divide the value by a prime number which divides equally into it. It’s most convenient to begin 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 here.
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 earlier worked through a few examples, let’s do another one using 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.
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? Nope.
What is a prime number that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number that 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 many practical applications in math. One of the primary applications is streamlining fractions. By finding the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and streamline 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 streamlined fraction of 1/3.
To check how this functions, 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
Next, we rule 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 also executes an essential role in cryptography and computer science. As you proceed in progressive math and science concepts, you will find further uses for prime factorization and be pleased you are an expert.
It’s Peak Hour to Enhance Your Mathematical Abilities
Prime factorization is an important theory in mathematics that enables us to simplify equations and fractions, moreover understand the properties of a number. By practicing and comprehending the methods and uses of prime factorization, we could improve our mathematical abilities and analytical abilities.
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