Finding the Highest Common Factor (HCF)

Introduction

• The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest factor that a set of numbers has in common.
• Typically, you will find the HCF for a pair of numbers.

Finding HCF by Listing Factors

• Example: 20 and 28

  • Factors of 20: 1, 2, 4, 5, 10, 20
  • Factors of 28: 1, 2, 4, 7, 14, 28
  • Common factors: 1, 2, 4
  • HCF: 4 (largest common factor)

• Example: 12 and 18

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18
  • Common factors: 1, 2, 3, 6
  • HCF: 6

Finding HCF Using Prime Factors

• Method:

  1. Determine the prime factors of each number.
  2. Select only the common prime factors.
  3. Multiply these common prime factors together to find the HCF.

• Example: 12 and 18

  • Prime factors of 12: 2, 2, 3
  • Prime factors of 18: 2, 3, 3
  • Common prime factors: 2, 3
  • HCF: 2 * 3 = 6

• Note on Repeated Factors:

  • If a number appears more than once in both lists, include it the number of times it appears.
  • Example: 12 and 20
    • Change 18 to 20
    • Prime factors of 20: 2, 2, 5
    • Common factors: 2, 2
    • HCF: 2 * 2 = 4

Practice Examples

• Example: 28 and 42

  • Prime factors of 28: 2, 2, 7
  • Prime factors of 42: 2, 3, 7
  • Common prime factors: 2, 7
  • HCF: 2 * 7 = 14

• Example: 132 and 420

  • Common prime factors: 2, 2, 3
  • HCF: 2 * 2 * 3 = 12

Conclusion

• These methods help in efficiently finding the HCF of two numbers.
• Practice these techniques for a better understanding.
• End of video.