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101 LearnersLast updated on September 25, 2025
Math Formula for HCF
In mathematics, the Highest Common Factor (HCF), also known as the greatest common divisor (GCD), is the largest number that divides two or more integers without leaving a remainder. In this topic, we will learn how to calculate the HCF using different methods.
List of Math Formulas for HCF
The HCF of two or more numbers can be determined using different methods. Let’s learn the formulas and techniques to calculate the HCF.
Math Formula for HCF using Prime Factorization
The HCF of two numbers can be calculated by finding the prime factors of each number, then identifying the common factors, and multiplying them to get the HCF.
1. Find the prime factors of each number.
2. Identify the common prime factors.
3. Multiply the common prime factors to get the HCF.
Math Formula for HCF using Division Method
The division method involves repeatedly dividing the larger number by the smaller number and continuing this process until the remainder is zero. The last non-zero remainder is the HCF. Steps for the division method:
1. Divide the larger number by the smaller number
. 2. Use the remainder as the new divisor and the previous divisor as the new dividend.
3. Repeat the process until the remainder is zero.
4. The last non-zero remainder is the HCF.
Math Formula for HCF using Euclidean Algorithm
The Euclidean algorithm is an efficient way to calculate the HCF. It uses a series of divisions to find the HCF. Steps for the Euclidean algorithm:
1. Divide the larger number by the smaller number.
2. Replace the larger number with the smaller number and the smaller number with the remainder.
3. Repeat the process until the remainder is zero.
4. The last non-zero remainder is the HCF.
Importance of HCF
The HCF is important in mathematics and real life because it helps in simplifying fractions, solving problems involving ratios, and other applications.
Here are some key points about the importance of HCF:
- It is used to simplify fractions to their lowest form.
- It helps in solving problems related to ratios and proportions.
- It is useful in finding the smallest dimensions of a shape or an object that can be measured using whole numbers.
Tips and Tricks to Memorize HCF Calculation Methods
Students may find calculating HCF challenging, so here are some tips and tricks to master HCF calculation methods:
- Practice regularly with different sets of numbers to become familiar with the methods.
- Use mnemonic devices to remember the steps for each method.
- Create a flowchart of the steps involved in each method for easy reference.
Common Mistakes and How to Avoid Them While Calculating HCF
Students make errors when calculating HCF. Here are some mistakes and the ways to avoid them to master HCF calculations.
Mistake 1
Not Identifying All Prime Factors
Students sometimes miss some prime factors when using the prime factorization method.
To avoid this error, ensure that all prime factors are identified and listed for each number.
Mistake 2
Confusing HCF with LCM
Students often confuse HCF with the least common multiple (LCM).
To avoid this confusion, remember that HCF is the largest number dividing all numbers, while LCM is the smallest number that is a multiple of all numbers.
Mistake 3
Incorrect Division in the Division Method
Errors can occur in the division process when using the division method.
To avoid these mistakes, double-check each division step to ensure accuracy.
Mistake 4
Skipping Steps in the Euclidean Algorithm
Students may skip steps or perform the Euclidean algorithm incorrectly.
To avoid this, follow each step carefully and ensure the remainder is used correctly in each iteration.
Examples of Problems Using HCF Formulas
Problem 1
Find the HCF of 24 and 36 using the prime factorization method.
The HCF is 12
Explanation
Prime factors of 24: 2 × 2 × 2 × 3
Prime factors of 36: 2 × 2 × 3 × 3
Common prime factors: 2 × 2 × 3
HCF = 2 × 2 × 3 = 12
Problem 2
Find the HCF of 56 and 98 using the division method.
The HCF is 14
Explanation
Divide 98 by 56, remainder is 42.
Divide 56 by 42, remainder is 14.
Divide 42 by 14, remainder is 0.
The last non-zero remainder is 14, which is the HCF.
Problem 3
Find the HCF of 48 and 180 using the Euclidean algorithm.
The HCF is 12
Explanation
Divide 180 by 48, remainder is 36.
Divide 48 by 36, remainder is 12.
Divide 36 by 12, remainder is 0.
The last non-zero remainder is 12, which is the HCF.
FAQs on HCF Calculation Methods
1.What is the HCF?
2.How is the HCF different from the LCM?
3.How do you find the HCF using the Euclidean algorithm?
4.What is the HCF of 15 and 45 using the division method?
5.Why is finding the HCF important?
Glossary for HCF Calculation Methods
- HCF: The Highest Common Factor, the largest number that divides two or more numbers without a remainder.
- Prime Factorization: A method of expressing a number as a product of its prime factors.
- Division Method: A technique for finding the HCF by dividing the larger number by the smaller number repeatedly.
- Euclidean Algorithm: An efficient method to find the HCF using a series of divisions.
- Remainder: The amount left over after division when one number does not divide another exactly.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
