Objective:
Determine the Highest Common Factor (HCF) for the integers 132 and 77.
Definition of HCF
The HCF, also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more integers without leaving a remainder.
Prime Factorization
Prime factors of 132:
132 = 2 × 2 × 3 × 11 = \(2^2 \times 3 \times 11\)
Prime factors of 77:
77 = 7 × 11 = \(7 \times 11\)
Common Prime Factors Identification
- Factors of 132: \(2^2, 3, 11\)
- Factors of 77: \(7, 11\)
The shared prime factor is 11.
Conclusion:
The HCF of 132 and 77 is 11.