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2 <p>Last updated on<strong>September 25, 2025</strong></p>

3 <p>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.</p>

4 <h2>List of Math Formulas for HCF</h2>

5 <p>The HCF of two or more<a>numbers</a>can be determined using different methods. Let’s learn the<a>formulas</a>and techniques to calculate the HCF.</p>

6 <h2>Math Formula for HCF using Prime Factorization</h2>

7 <p>The HCF of two numbers can be calculated by finding the<a>prime factors</a>of each number, then identifying the<a>common factors</a>, and multiplying them to get the HCF.</p>

8 <p>1. Find the prime factors of each number.</p>

9 <p>2. Identify the common prime factors.</p>

10 <p>3. Multiply the common prime factors to get the HCF.</p>

11 <h2>Math Formula for HCF using Division Method</h2>

12 <p>The<a>division</a>method involves repeatedly dividing the larger number by the smaller number and continuing this process until the<a>remainder</a>is zero. The last non-zero remainder is the HCF. Steps for the division method:</p>

13 <p>1. Divide the larger number by the smaller number</p>

14 <p>. 2. Use the remainder as the new<a>divisor</a>and the previous divisor as the new<a>dividend</a>.</p>

15 <p>3. Repeat the process until the remainder is zero.</p>

16 <p>4. The last non-zero remainder is the HCF.</p>

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19 <h2>Math Formula for HCF using Euclidean Algorithm</h2>

18 <h2>Math Formula for HCF using Euclidean Algorithm</h2>

20 <p>The<a>Euclidean algorithm</a>is an efficient way to calculate the HCF. It uses a<a>series</a>of divisions to find the HCF. Steps for the Euclidean algorithm:</p>

19 <p>The<a>Euclidean algorithm</a>is an efficient way to calculate the HCF. It uses a<a>series</a>of divisions to find the HCF. Steps for the Euclidean algorithm:</p>

21 <p>1. Divide the larger number by the smaller number.</p>

20 <p>1. Divide the larger number by the smaller number.</p>

22 <p>2. Replace the larger number with the smaller number and the smaller number with the remainder.</p>

21 <p>2. Replace the larger number with the smaller number and the smaller number with the remainder.</p>

23 <p>3. Repeat the process until the remainder is zero.</p>

22 <p>3. Repeat the process until the remainder is zero.</p>

24 <p>4. The last non-zero remainder is the HCF.</p>

23 <p>4. The last non-zero remainder is the HCF.</p>

25 <h2>Importance of HCF</h2>

24 <h2>Importance of HCF</h2>

26 <p>The HCF is important in mathematics and real life because it helps in<a>simplifying fractions</a>, solving problems involving<a>ratios</a>, and other applications.</p>

25 <p>The HCF is important in mathematics and real life because it helps in<a>simplifying fractions</a>, solving problems involving<a>ratios</a>, and other applications.</p>

27 <p>Here are some key points about the importance of HCF: </p>

26 <p>Here are some key points about the importance of HCF: </p>

28 <ul><li>It is used to simplify fractions to their lowest form. </li>

27 <ul><li>It is used to simplify fractions to their lowest form. </li>

29 <li>It helps in solving problems related to ratios and proportions. </li>

28 <li>It helps in solving problems related to ratios and proportions. </li>

30 <li>It is useful in finding the smallest dimensions of a shape or an object that can be measured using<a>whole numbers</a>.</li>

29 <li>It is useful in finding the smallest dimensions of a shape or an object that can be measured using<a>whole numbers</a>.</li>

31 </ul><h2>Tips and Tricks to Memorize HCF Calculation Methods</h2>

30 </ul><h2>Tips and Tricks to Memorize HCF Calculation Methods</h2>

32 <p>Students may find calculating HCF challenging, so here are some tips and tricks to master HCF calculation methods: </p>

31 <p>Students may find calculating HCF challenging, so here are some tips and tricks to master HCF calculation methods: </p>

33 <ul><li>Practice regularly with different<a>sets</a>of numbers to become familiar with the methods. </li>

32 <ul><li>Practice regularly with different<a>sets</a>of numbers to become familiar with the methods. </li>

34 <li>Use mnemonic devices to remember the steps for each method. </li>

33 <li>Use mnemonic devices to remember the steps for each method. </li>

35 <li>Create a flowchart of the steps involved in each method for easy reference.</li>

34 <li>Create a flowchart of the steps involved in each method for easy reference.</li>

36 </ul><h2>Common Mistakes and How to Avoid Them While Calculating HCF</h2>

35 </ul><h2>Common Mistakes and How to Avoid Them While Calculating HCF</h2>

37 <p>Students make errors when calculating HCF. Here are some mistakes and the ways to avoid them to master HCF calculations.</p>

36 <p>Students make errors when calculating HCF. Here are some mistakes and the ways to avoid them to master HCF calculations.</p>

38 <h3>Problem 1</h3>

37 <h3>Problem 1</h3>

39 <p>Find the HCF of 24 and 36 using the prime factorization method.</p>

38 <p>Find the HCF of 24 and 36 using the prime factorization method.</p>

40 <p>Okay, lets begin</p>

39 <p>Okay, lets begin</p>

41 <p>The HCF is 12</p>

40 <p>The HCF is 12</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>Prime factors of 24: 2 × 2 × 2 × 3</p>

42 <p>Prime factors of 24: 2 × 2 × 2 × 3</p>

44 <p>Prime factors of 36: 2 × 2 × 3 × 3</p>

43 <p>Prime factors of 36: 2 × 2 × 3 × 3</p>

45 <p>Common prime factors: 2 × 2 × 3</p>

44 <p>Common prime factors: 2 × 2 × 3</p>

46 <p>HCF = 2 × 2 × 3 = 12</p>

45 <p>HCF = 2 × 2 × 3 = 12</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

47 <h3>Problem 2</h3>

49 <p>Find the HCF of 56 and 98 using the division method.</p>

48 <p>Find the HCF of 56 and 98 using the division method.</p>

50 <p>Okay, lets begin</p>

49 <p>Okay, lets begin</p>

51 <p>The HCF is 14</p>

50 <p>The HCF is 14</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>Divide 98 by 56, remainder is 42.</p>

52 <p>Divide 98 by 56, remainder is 42.</p>

54 <p>Divide 56 by 42, remainder is 14.</p>

53 <p>Divide 56 by 42, remainder is 14.</p>

55 <p>Divide 42 by 14, remainder is 0.</p>

54 <p>Divide 42 by 14, remainder is 0.</p>

56 <p>The last non-zero remainder is 14, which is the HCF.</p>

55 <p>The last non-zero remainder is 14, which is the HCF.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 3</h3>

57 <h3>Problem 3</h3>

59 <p>Find the HCF of 48 and 180 using the Euclidean algorithm.</p>

58 <p>Find the HCF of 48 and 180 using the Euclidean algorithm.</p>

60 <p>Okay, lets begin</p>

59 <p>Okay, lets begin</p>

61 <p>The HCF is 12</p>

60 <p>The HCF is 12</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>Divide 180 by 48, remainder is 36.</p>

62 <p>Divide 180 by 48, remainder is 36.</p>

64 <p>Divide 48 by 36, remainder is 12.</p>

63 <p>Divide 48 by 36, remainder is 12.</p>

65 <p>Divide 36 by 12, remainder is 0.</p>

64 <p>Divide 36 by 12, remainder is 0.</p>

66 <p>The last non-zero remainder is 12, which is the HCF.</p>

65 <p>The last non-zero remainder is 12, which is the HCF.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h2>FAQs on HCF Calculation Methods</h2>

67 <h2>FAQs on HCF Calculation Methods</h2>

69 <h3>1.What is the HCF?</h3>

68 <h3>1.What is the HCF?</h3>

70 <p>The HCF, or Highest Common Factor, is the largest number that divides two or more<a>integers</a>without leaving a remainder.</p>

69 <p>The HCF, or Highest Common Factor, is the largest number that divides two or more<a>integers</a>without leaving a remainder.</p>

71 <h3>2.How is the HCF different from the LCM?</h3>

70 <h3>2.How is the HCF different from the LCM?</h3>

72 <h3>3.How do you find the HCF using the Euclidean algorithm?</h3>

71 <h3>3.How do you find the HCF using the Euclidean algorithm?</h3>

73 <p>To find the HCF using the Euclidean algorithm, divide the larger number by the smaller number, replace the larger with the smaller, and the smaller with the remainder. Repeat until the remainder is zero. The last non-zero remainder is the HCF.</p>

72 <p>To find the HCF using the Euclidean algorithm, divide the larger number by the smaller number, replace the larger with the smaller, and the smaller with the remainder. Repeat until the remainder is zero. The last non-zero remainder is the HCF.</p>

74 <h3>4.What is the HCF of 15 and 45 using the division method?</h3>

73 <h3>4.What is the HCF of 15 and 45 using the division method?</h3>

75 <p>The HCF of 15 and 45 is 15.</p>

74 <p>The HCF of 15 and 45 is 15.</p>

76 <h3>5.Why is finding the HCF important?</h3>

75 <h3>5.Why is finding the HCF important?</h3>

77 <p>Finding the HCF is important for simplifying<a>fractions</a>, solving problems involving ratios, and in various real-life applications such as dividing resources evenly.</p>

76 <p>Finding the HCF is important for simplifying<a>fractions</a>, solving problems involving ratios, and in various real-life applications such as dividing resources evenly.</p>

78 <h2>Glossary for HCF Calculation Methods</h2>

77 <h2>Glossary for HCF Calculation Methods</h2>

79 <ul><li><strong>HCF:</strong>The Highest Common Factor, the largest number that divides two or more numbers without a remainder.</li>

78 <ul><li><strong>HCF:</strong>The Highest Common Factor, the largest number that divides two or more numbers without a remainder.</li>

80 </ul><ul><li><strong>Prime Factorization:</strong>A method of expressing a number as a<a>product</a>of its prime factors.</li>

79 </ul><ul><li><strong>Prime Factorization:</strong>A method of expressing a number as a<a>product</a>of its prime factors.</li>

81 </ul><ul><li><strong>Division Method:</strong>A technique for finding the HCF by dividing the larger number by the smaller number repeatedly.</li>

80 </ul><ul><li><strong>Division Method:</strong>A technique for finding the HCF by dividing the larger number by the smaller number repeatedly.</li>

82 </ul><ul><li><strong>Euclidean Algorithm:</strong>An efficient method to find the HCF using a series of divisions.</li>

81 </ul><ul><li><strong>Euclidean Algorithm:</strong>An efficient method to find the HCF using a series of divisions.</li>

83 </ul><ul><li><strong>Remainder:</strong>The amount left over after division when one number does not divide another exactly.</li>

82 </ul><ul><li><strong>Remainder:</strong>The amount left over after division when one number does not divide another exactly.</li>

84 </ul><h2>Jaskaran Singh Saluja</h2>

83 </ul><h2>Jaskaran Singh Saluja</h2>

85 <h3>About the Author</h3>

84 <h3>About the Author</h3>

86 <p>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.</p>

85 <p>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.</p>

87 <h3>Fun Fact</h3>

86 <h3>Fun Fact</h3>

88 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>

87 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>