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, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we can streamline fractions and equations, also learn the properties of that number. Let’s get a closer look.
Methods for Determining Prime Factorization
There are two primary processes for working out prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other methods will grant you the exact answer.
Factor Tree Method
The primary way 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.
Below it, create branches for the factors.
Proceed by making branches and factoring before you arrive at a prime number.
Here’s an instance of the thought process:
We recognize that 6 * 6 = 36.
Is 6 a prime number? No. 2 * 3 = 6.
Are 2 and 3 prime numbers? Yes. We have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To imagine this procedure, we could create a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is figured out by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The second method for finding the prime factorization of a number is to begin using a record of prime numbers. Write down the value you are attempting to factor. Subsequently, divide the number by a prime number that divides equally into it. It’s simplest to start 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 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? Nope.
What is a prime number that 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 methods, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked through a some examples, let’s do another one using both processes.
Let’s utilize 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 done.
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 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? Nope.
What is a prime number which 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.
Utilizations of Prime Factorization
Prime factorization has many realistic uses in math. One of the major applications 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 clarify 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 functions, 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
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 streamlined fraction of 1/3.
Prime factorization further executes an important part in computer science and cryptography. As you go ahead in progressive math and science concepts, you will find additional applications for prime factorization and be delighted you are a pro.
It’s Prime Time to Boost Your Mathematical Abilities
Prime factorization is a crucial concept in math which allows us to streamline equations and fractions, moreover learn the characteristics of a number. By practicing and comprehending the processes and uses of prime factorization, we can improve our math abilities and problem-solving skills.
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