Prime Time | Class 6 Mathematics Notes

Highest Common Factor (HCF)

This section explains the Highest Common Factor (HCF), which is the greatest number that divides two or more numbers exactly without leaving a remainder. The HCF is useful in simplifying fractions, solving problems involving divisibility, and finding common measures. The section describes methods to find the HCF, including listing factors, prime factorization, and the division method. Using prime factorization, the HCF is found by multiplying the common prime factors with the smallest powers. For example, to find the HCF of 24 and 36, prime factorize both: 24 = 2³ × 3, 36 = 2² × 3²; common prime factors are 2² and 3, so HCF = 2² × 3 = 12. The section provides detailed examples and emphasizes the importance of HCF in real-life contexts such as arranging objects in groups or dividing things equally.

📊 Diagram: Figure 6 on page 7 illustrates the division method to find HCF; Table on page 7 (9×10) lists numbers 1 to 100 to assist factor identification.

🧪 Activity: Students find HCF of pairs of numbers using prime factorization and division methods.

🔗 Connection: This section connects to 'Least Common Multiple (LCM),' which complements HCF in understanding number relationships.

Table on page 7 (9×10)