Lecture Notes: Highest Common Factor (HCF)

Introduction to HCF

• Definition: The Highest Common Factor (HCF) is the largest factor that two or more numbers have in common.
• Typically, problems will involve finding the HCF of a pair of numbers.

Method 1: Listing Factors

1. Example: Finding HCF of 20 and 28.

   • Factors of 20: 1, 2, 4, 5, 10, 20
   • Factors of 28: 1, 2, 4, 7, 14, 28
   • HCF: The largest common factor is 4.

2. Example: Finding HCF of 12 and 18.

   • Factors of 12: 1, 2, 3, 4, 6, 12
   • Factors of 18: 1, 2, 3, 6, 9, 18
   • HCF: The largest common factor is 6.

Method 2: Using Prime Factors

• Process:
  1. Determine the prime factors of each number.
  2. Identify the common prime factors.
  3. Multiply these common prime factors to find the HCF.

Detailed Example

• Finding HCF using prime factors for 12 and 18:

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

• Using prime factors for 20 and 28:

  • Prime factors of 20: 2, 2, 5
  • Prime factors of 28: 2, 2, 7
  • Common prime factors: 2, 2
  • HCF: 2 x 2 = 4

Practice Example

• Finding HCF of 28 and 42:
  • Prime factors of 28 and 42 include 2 and 7
  • HCF: 2 x 7 = 14

Another Example

• Finding HCF of 132 and 420:
  • Common prime factors: 2, 2, 3
  • HCF: 2 x 2 x 3 = 12

Conclusion

• Understanding both methods (listing factors and using prime factors) provides a comprehensive approach to finding the HCF.
• Practice with different examples to improve accuracy and speed.

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This concludes the lecture on finding the Highest Common Factor. Practice these methods to become proficient in calculating the HCF of any given numbers.