Highest Common Factor

In mathematics, one of the most important concepts that students learn is how to find the highest common factor (HCF). This skill is essential for completing many different types of math problems. In this blog post, we will provide a guide on how to find the HCF of two or more numbers. We will also provide an HCF calculator that students can use to practice this skill. 

Highest Common Factor

The HCF, or Highest Common Factor, is the largest number that will divide evenly into two or more other numbers. Finding the HCF is an important skill in number theory and is used by many students in subjects like algebra, geometry, and calculus. HCF problems can be solved using an HCF calculator or by hand. In this article, we will show you how to find the HCF by hand because you are not going to get the HCF calculator in your exam.

Properties of HCF

The HCF is the largest number that divides evenly into two or more other numbers. The HCF is also unique, so there can only be one HCF for any given set of numbers.

Difference between GCD and HCF

The greatest common divisor (GCD) of two or more numbers is the largest number that divides evenly into all of them. The HCF and GCD are different names for the same thing. The HCF is the most common factor, while the GCD is the largest one.

Therefore, there is no difference between GCD and HCF.

How to find HCF?

Finding the HCF (highest common factor) of two or more numbers is a useful skill for mathematics students. The HCF is the largest number that evenly divides all of the other numbers. In other words, it’s the greatest number that can be divided by each of the others without any remainder.

There are a few different methods that can be used to find the HCF. One method is to use a calculator, and another is to use prime factorization.

The easiest way to find the HCF using a calculator is to use the “prime factorization” function. This will break each number down into its prime factors (the numbers that are multiplied together to create the original number). Once the prime factors are known, the HCF can be easily calculated by finding the largest number that is a factor of all of the others.

Prime Factorisation method

Begin by dividing the given numbers by 2 (the first prime number), then continue dividing until you can no longer divide the number.

Finally, write the numbers as a prime number product. The highest common factor of the supplied numbers is the product of these common factors.

Factorization Method

HCF of two numbers is the product of common prime factors with minimum powers. For example HCF(12, 18) = HCF[(21 x 32), (22 x 33)] = 22 = 22 × 31= 42

Steps to calculate HCF using Factorization Method :

• List down all the prime factors of both the numbers
• Compare the prime factors and find the common ones
• Write down these common prime factors with their respective powers
• The HCF of two numbers is the product of common prime factors with minimum powers

Division method

To calculate the HCF of two or more numbers, follow these steps:

Step One: Write down all of the numbers that you are working with.

Step Two: Divide each number by the HCF of all of the numbers that you are working with except for itself. Write down the resulting quotients next to their corresponding numbers.

Step Three: Write down each HCF of all the quotients that you calculated in step two, along with their corresponding remainder(s).

Step Four: Solve for HCF by multiplying the HCF and adding any remainders together. The result should be your HCF! Here is an example:

To calculate the HCF of 15 and 30, follow these steps:

Step One: Write down all of the numbers that you are working with.

15 and 30

Step Two: Divide each number by the HCF of all of the numbers that you are working with except for itself. Write down the resulting quotients next to their corresponding numbers.

15/30 = 0.50 (remainder 15)

30/15 = HCF(0.33) + HCF(0.17), or HCF(0.66 + HCF(0))

 Note: You only need to calculate HCF once for each number.

Step Three: Write down each HCF of all the quotients that you calculated in step two, along with their corresponding remainders. HCF(0) = 0 and HCF(0.66) = 0

Step Four: Solve for HCF by multiplying the HCF and adding any remainders together. HCF(15, 30) = HCF(0.66 + 0) = HCF(0.66), or simply HCF(30, 15) = HCF(15, 15).

The final answer is the HCF of 30 and 15 is 15.

You can also use the Euclidean algorithm to calculate HCF:

This method is actually quite simple. You simply divide one number by another and then take the remainder as your answer!

Conclusion

In order to find the highest common factor, you will need a list of all the numbers that are being multiplied together. The product of these numbers is then reduced until it reaches 1. For example, if we were looking for the HCF between 12 and 18, we would follow this process: 3 x 4 = 12; 2 x 6 = 12; 5 x 9 = 45 which reduces to 13 as well as 45 both equal one when divided by any number other than themselves. This means that at least one factor from each column needs to be included in our equation so they can cancel out once their product has been calculated. If there is only one number left after going through this process-for example with 24 and 36-then that number is the HCF. Otherwise, whichever number has the smallest product remaining is your HCF.