Question
Download Solution PDFयदि 5 अंकों की संख्या 676xy, 3, 7 और 11 से विभाज्य है, तो (3x - 5y) का मान क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
676xy, 3, 7 और 11 से विभाज्य है।
अवधारणा:
जब 676xy, 3, 7 और 11 से विभाज्य है, तो यह 3, 7 और 11 के लघुत्तम समापवर्त्य से भी विभाज्य होगा।
भाज्य = भाजक × भागफल + शेषफल
गणना:
(3, 7, 11) लघुत्तम समापवर्त्य = 231
5 अंकों की सबसे बड़ी संख्या 67699 लेकर उसे 231 से भाग देने पर।
∵ 67699 = 231 × 293 + 16
⇒ 67699 = 67683 + 16
⇒ 67699 - 16 = 67683 (231 से पूर्णतः विभाज्य)
∴ 67683 = 676xy (जहाँ x = 8, y = 3)
(3x - 5y) = 3 × 8 - 5 × 3
⇒ 24 - 15 = 9
∴ अभीष्ट परिणाम = 9
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