Question:
What is the greatest number that will divide 148, 246, and 623 leaving remainders 4, 6, and 11 respectively?
वह सबसे बड़ी संख्या क्या है जो 148, 246 और 623 को विभाजित करने पर क्रमशः 4, 6 और 11 शेषफल छोड़ती है?
Options:
- 12
- 16
- 18
- 24
- 12
- 16
- 18
- 24
Correct Answer: a)
Explanation:
Required number = \(\text{HCF}(148 – 4, 246 – 6, 623 – 11) = \text{HCF}(144, 240, 612)\).
\(\text{HCF}(144, 240) = 48\).
\(\text{HCF}(48, 612)\): \(612 = 48 \times 12 + 36\); \(48 = 36 \times 1 + 12\); \(36 = 12 \times 3 + 0\).
HCF = 12.
\(\text{HCF}(144, 240) = 48\).
\(\text{HCF}(48, 612)\): \(612 = 48 \times 12 + 36\); \(48 = 36 \times 1 + 12\); \(36 = 12 \times 3 + 0\).
HCF = 12.
संख्या = HCF(144, 240, 612) = 12।