Prime Factorization is a mathematical function employed to split up a composite number into its prime factors. Composite numbers could 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, such as 2, 3, 5, and 7.
By figuring out the prime factors of a number, we could streamline equations and fractions, in addition understand the characteristics of that number. Let’s take a closer look.
Ways for Figuring out Prime Factorization
There are two main ways for working out prime factorization. You could utilize a factor tree, or you can factor by dividing by prime numbers. One as well as the other methods will give you the exact outcome.
Factor Tree Method
The first way is utilizing a factor tree. To create a factor tree:
Initiate by writing the number you are attempting to factor at the top of the page.
Underneath, make branches for the factors.
Proceed by creating branches and factoring before 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.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this process, we can make a factor tree for 36 as ensues.
As you can see, the prime factorization of 36 is comprehended by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second way for finding the prime factorization of a number is to begin utilizing a list of prime numbers. Note the value you are attempting to factor. Subsequently, divide the value by a prime number which divides equally into it. It’s simplest to begin with the first 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? Nope.
What is a prime number that divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? Nope.
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 process, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Although we’ve already worked through a some examples, let’s do one more utilizing both processes.
Let’s use a factor tree to find 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 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? Nope.
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.
Uses of Prime Factorization
Prime factorization has multiple practical uses in mathematics. One of the major 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 simplify the fraction.
For instance, the fraction 8/24 could be simplified 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 clarified fraction of 1/3.
To check how this works, let's use 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
Subsequently, we rule out ever 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 streamlined fraction of 1/3.
Prime factorization also plays an important role in computer science and cryptography. As you proceed in advanced math and science concepts, you will figure out more applications for prime factorization and be pleased you are a professional.
It’s Prime Time to Advance Your Math Abilities
Prime factorization is an essential theory in math that enables us to streamline equations and fractions, also learn the characteristics of a number. By practicing and comprehending the processes and applications of prime factorization, we can improve our math skills and analytical skills.
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