Question:
The HCF of \(2^3 \times 3^3 \times 5^2 \times 11\) and \(2 \times 3 \times 5 \times 7 \times 11^2\) is:
\(2^3 \times 3^3 \times 5^2 \times 11\) और \(2 \times 3 \times 5 \times 7 \times 11^2\) का म.स.प. (HCF) क्या है?
Options:
- 2×3×5
- 3×5×11
- 2×3×5×11
- 3×11
- 2×3×5
- 3×5×11
- 2×3×5×11
- 3×11
Correct Answer: c)
Explanation:
The HCF is the product of the lowest powers of common prime factors:
Common primes: 2, 3, 5, 11.
\(\text{HCF} = 2^{\min(3,1)} \times 3^{\min(3,1)} \times 5^{\min(2,1)} \times 11^{\min(1,2)} = 2^1 \times 3^1 \times 5^1 \times 11^1 = 2 \times 3 \times 5 \times 11\).
उभयनिष्ठ अभाज्य गुणनखंडों की न्यूनतम घातों का गुणनफल HCF होता है:
\(\text{HCF} = 2^1 \times 3^1 \times 5^1 \times 11^1 = 2 \times 3 \times 5 \times 11\)। अतः विकल्प (c) सही है।