How to Find the Prime Factorization of 24 Easily
- Author: Noreen Niazi
- Last Updated on: December 19, 2023
Introduction to Prime Factorization
The process of prime factorization entails dividing a composite number into its prime elements. Any number higher than 1 that can be divided by at least two different numbers in addition to itself and one is said to be a composite number. The term “prime factor” refers to a prime number that may be divided into the original number without leaving a remainder. A prime number is one that can be divided only by one and by itself.
What is the Prime Factorization of 24?
We must divide 24 into its prime elements in order to determine the prime factorization. The composite number 24 can be split by several different integers in an even number of parts. Divide 24 by the smallest prime number, 2, to begin identifying the prime factors that makeup 24.
The result of 24 divided by 2 is 12, which is also a composite number. Twelve can be split by two more times to reach the number six. 6 can be split by 2 once more to get 3. Since 3 is a prime number, we can cease diving it.
As a result, the prime factorization of 24 is 2 x 2 x 2 x 3, or 23 x 3.[1].
Prime Factorization Method
The prime factorization method involves breaking down a composite number into its prime factors. To use this method, you must find the smallest prime number that can divide into the composite number evenly. Then, divide the result by the smallest prime number until you get a prime number.
Let’s use this method to find the prime factorization of 24.
- Start with the smallest prime number, which is 2.
- Divide 24 by 2 to get 12.
- Since 12 is also a composite number, divide it by 2 again to get 6.
- Divide 6 by 2 to get 3.
- 3 is a prime number, so we can stop dividing.
Therefore, the prime factorization of 24 is 2³ x 3.
Divisibility Rules for Prime Factorization
Divisibility rules help you quickly determine if a number is divisible by another number. These rules can be helpful when using the prime factorization method.
An integer, for instance, is divisible by two if the last digit is even. If a number can be divided by three, then its digit sum can also. If a number’s last digit is either 0 or 5, it can be divided by five.
Using these rules can save you time when finding the prime factorization of a number.
Prime Factorization of 24 Using a Factor Tree
A factor tree is a visual method for finding the prime factorization of a number. To use a factor tree to find the prime factorization of 24, follow these steps[2]:
- Start with the number 24 and draw a circle around it.
- Find two factors of 24 that multiply to equal 24. In this case, the factors are 2 and 12. Write these factors on branches stemming from the circle.
- Continue to break down each factor until you reach a prime number.
- The prime factors of 24 are 2, 2, 2, and 3.
Prime Factorization of 24 Using a Calculator
If you have a scientific calculator, you can quickly find the prime factorization of 24[3]. Follow these steps:
- Enter the number 24 into the calculator.
- Press the prime factorization button.
- The calculator will display the prime factorization of 24 as 2³ x 3.
Prime Factorization of 24 Using Division Method
To use the division method to find the prime factorization of 24, follow these steps:
- Write down 24 and divide it by the smallest prime number, 2.
- Write down the result of the division and divide it by the smallest prime number again. Continue this process until you reach a prime number.
- The prime factors 24 are 2, 2, 2, and 3.
How to Check if You Have the Correct Prime Factorization of 24?
Once you get to know about the prime factors, the next step is to determine whether it’s right or not. You can easily verify it by multiplying prime factors together, if comes out 24, that means you are right.
Let’s multiply the factors together.
2 x 2 x 2 x 3 = 24
It is necessary to go back and review your work if the product of the prime factors does not equal the starting value.
Applications of Prime Factorization of 24
Mathematicians can use prime factorization for various tasks, including factoring equations, finding common denominators, and simplifying fractions.
For example,
Simplify the fraction 12/24.
We can use the prime factorization of 24 to find the greatest common factor for simplifying a given fraction.
The prime factorization of 24 is 2³ x 3.
The prime factorization of 12 is 2² x 3.
The greatest common factor is 2² x 3, which is 12.
Dividing the fraction’s numerator and denominator by 12 gives 1/2, which is the simplified form of the fraction.
Conclusion
In mathematics, the idea of prime factorization is helpful and can make problems considerably simpler to solve. There are various ways to determine the prime factorization of 24, including the prime factorization method, factor tree, calculator, and division method. Once you have identified the prime factors, you may verify your work by multiplying them by the original number to ensure they are equivalent.
Remember that prime factorization has several applications in math, so it’s important to understand this concept thoroughly.
FAQ - Prime Factorization
- What is prime factorization?
Prime factorization is breaking down a composite number into its prime factors.
- What is a composite number?
A composite number is greater than one that can be divided by at least one other number besides itself and 1.
- What are prime factors?
Prime factors are prime numbers that can divide into the original number without a remainder.
- What is a prime number?
A prime number is a number that is only divisible by one and itself.
- How can I determine a number’s prime factorization?
Divide any number by the smallest prime number to get its prime factorization, then keep doing so until you reach prime numbers that cannot be further divided.
- How do I determine 24’s prime factorization?
We divide 24 by the smallest prime number, 2, to obtain the prime factorization of that integer. We divide the resulting quotient again until we arrive at a prime number. 24 can be factorised as 2 x 2 x 2 x 3, or $$2^3 x 3$$.
- Is it possible for a number to have several prime factors?
No, a number can only be factorized into one distinct prime.
- Is it possible to prime factorize any composite number?
Yes, it is possible to decompose every composite number into its prime components.
- What is the benefit of prime factorization?
Numerous mathematical operations, including determining the greatest common factor or simplifying square roots, might benefit from the prime factorization.
- Is there a particular prime factorization technique?
Yes, the typical approach to prime factorization entails splitting the initial number into smaller primes and keeping on until you hit prime numbers that cannot be further divided. This approach makes it easier to determine the prime factorization efficiently.