If you’ve ever been perplexed by the highest common factor of 24 and 84, you’re not alone. Many people have difficulty understanding the concept and its application. In this blog post, we’ll be unlocking the mystery behind the highest common factor of 24 and 84. We’ll discuss how to calculate it, explain its importance, and provide examples of how it can be used in everyday life. By the end, you’ll understand the process behind this mathematical concept and be able to apply it to real-world situations.

Understanding Factors and Multiples

Understanding factors and multiples is key to unraveling the mystery behind the highest common factor of 24 and 84. Factors are numbers that can be multiplied together to obtain a given number. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Multiples, on the other hand, are numbers that are obtained by multiplying a given number by another whole number. For instance, the multiples of 24 include 24, 48, 72, and so on.

To find the highest common factor (HCF), we need to identify the factors that are common to both 24 and 84. These common factors are important because they help us determine the largest number that can divide evenly into both 24 and 84. By understanding factors and multiples, we can calculate the HCF and unlock its significance in solving various mathematical problems. Stay tuned as we dive deeper into finding the factors of 24 and uncover the common factors shared with 84.

Finding the Factors of 24

To find the factors of 24, we need to determine which numbers can be multiplied together to obtain 24. By examining the number 24, we can easily identify a few factors such as 1 and 24. However, to fully explore the factors of 24, we need to dive deeper. Dividing 24 by 2 gives us a quotient of 12, which means 2 is a factor of 24. Continuing this process, we can see that 3, 4, 6, and 8 are also factors of 24. Finally, when we divide 24 by 12, we get a quotient of 2, confirming that 12 is indeed a factor of 24 as well. So, to summarize, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Understanding these factors is crucial in unraveling the mystery behind the highest common factor of 24 and 84, as we’ll explore in the next section. Stay tuned!

Identifying Common Factors

Now that we have explored the factors of 24, it’s time to identify the common factors it shares with 84. By examining the factors of 24 and 84, we can start to unravel the mystery behind their highest common factor (HCF). To find the common factors, we need to compare the factors of 24 (1, 2, 3, 4, 6, 8, 12, and 24) with the factors of 84. This will help us determine which numbers are factors of both 24 and 84. By identifying the common factors, we can narrow down our search for the HCF. The common factors are crucial because they will ultimately lead us to the highest number that can divide evenly into both 24 and 84. In the next section, we’ll explore the calculations involved in finding the HCF and see how this concept is applicable to everyday life. Stay tuned!

Calculating the Highest Common Factor (HCF)

Now that we have explored the factors of 24 and identified the common factors it shares with 84, it’s time to calculate the highest common factor (HCF). To find the HCF, we need to determine the largest number that can evenly divide into both 24 and 84.

One way to calculate the HCF is by listing out the common factors and selecting the largest one. In this case, the common factors of 24 and 84 are 1, 2, 3, 4, 6, and 12. By examining these factors, we can see that the largest number that divides evenly into both 24 and 84 is 12. Therefore, the HCF of 24 and 84 is 12.

Another method to calculate the HCF is by using prime factorization. By finding the prime factors of 24 and 84, we can identify the common prime factors and multiply them together to obtain the HCF. In this case, the prime factors of 24 are 2, 2, 2, and 3, while the prime factors of 84 are 2, 2, 3, and 7. By multiplying the common prime factors, which are 2 and 3, we get the HCF of 24 and 84 as 6.

Calculating the HCF is an important mathematical concept that is applicable to various real-world situations. It helps us determine the greatest common divisor between two numbers, which can be useful in simplifying fractions, finding equivalent ratios, and solving problems in fields like engineering, finance, and computer science. Understanding how to calculate the HCF unlocks the mystery behind this mathematical concept and enables us to apply it confidently in everyday life. So, the next time you encounter the highest common factor of two numbers, you’ll know exactly how to calculate it and why it’s important.

## Answer ( 1 )

Mystery: The Highest Common Factor of 24 and 84If you’ve ever been perplexed by the highest common factor of 24 and 84, you’re not alone. Many people have difficulty understanding the concept and its application. In this blog post, we’ll be unlocking the mystery behind the highest common factor of 24 and 84. We’ll discuss how to calculate it, explain its importance, and provide examples of how it can be used in everyday life. By the end, you’ll understand the process behind this mathematical concept and be able to apply it to real-world situations.Understanding Factors and MultiplesUnderstanding factors and multiples is key to unraveling the mystery behind the highest common factor of 24 and 84. Factors are numbers that can be multiplied together to obtain a given number. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Multiples, on the other hand, are numbers that are obtained by multiplying a given number by another whole number. For instance, the multiples of 24 include 24, 48, 72, and so on.To find the highest common factor (HCF), we need to identify the factors that are common to both 24 and 84. These common factors are important because they help us determine the largest number that can divide evenly into both 24 and 84. By understanding factors and multiples, we can calculate the HCF and unlock its significance in solving various mathematical problems. Stay tuned as we dive deeper into finding the factors of 24 and uncover the common factors shared with 84.Finding the Factors of 24To find the factors of 24, we need to determine which numbers can be multiplied together to obtain 24. By examining the number 24, we can easily identify a few factors such as 1 and 24. However, to fully explore the factors of 24, we need to dive deeper. Dividing 24 by 2 gives us a quotient of 12, which means 2 is a factor of 24. Continuing this process, we can see that 3, 4, 6, and 8 are also factors of 24. Finally, when we divide 24 by 12, we get a quotient of 2, confirming that 12 is indeed a factor of 24 as well. So, to summarize, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Understanding these factors is crucial in unraveling the mystery behind the highest common factor of 24 and 84, as we’ll explore in the next section. Stay tuned!Identifying Common FactorsNow that we have explored the factors of 24, it’s time to identify the common factors it shares with 84. By examining the factors of 24 and 84, we can start to unravel the mystery behind their highest common factor (HCF). To find the common factors, we need to compare the factors of 24 (1, 2, 3, 4, 6, 8, 12, and 24) with the factors of 84. This will help us determine which numbers are factors of both 24 and 84. By identifying the common factors, we can narrow down our search for the HCF. The common factors are crucial because they will ultimately lead us to the highest number that can divide evenly into both 24 and 84. In the next section, we’ll explore the calculations involved in finding the HCF and see how this concept is applicable to everyday life. Stay tuned!Calculating the Highest Common Factor (HCF)Now that we have explored the factors of 24 and identified the common factors it shares with 84, it’s time to calculate the highest common factor (HCF). To find the HCF, we need to determine the largest number that can evenly divide into both 24 and 84.One way to calculate the HCF is by listing out the common factors and selecting the largest one. In this case, the common factors of 24 and 84 are 1, 2, 3, 4, 6, and 12. By examining these factors, we can see that the largest number that divides evenly into both 24 and 84 is 12. Therefore, the HCF of 24 and 84 is 12.Another method to calculate the HCF is by using prime factorization. By finding the prime factors of 24 and 84, we can identify the common prime factors and multiply them together to obtain the HCF. In this case, the prime factors of 24 are 2, 2, 2, and 3, while the prime factors of 84 are 2, 2, 3, and 7. By multiplying the common prime factors, which are 2 and 3, we get the HCF of 24 and 84 as 6.Calculating the HCF is an important mathematical concept that is applicable to various real-world situations. It helps us determine the greatest common divisor between two numbers, which can be useful in simplifying fractions, finding equivalent ratios, and solving problems in fields like engineering, finance, and computer science. Understanding how to calculate the HCF unlocks the mystery behind this mathematical concept and enables us to apply it confidently in everyday life. So, the next time you encounter the highest common factor of two numbers, you’ll know exactly how to calculate it and why it’s important.