Question
Download Solution PDFयदि 65 और 117 का महत्तम समापवर्तक 65m - 117 के रूप में व्यक्त किया जाता है, तो m का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यूक्लिड का विभाजन लेमा: दिए गए धनात्मक पूर्णांक a और b में पूर्ण संख्याएँ q और r संतुष्ट होती हैं,
a = bq + r, जहां, 0 ≤ r ≤ b
गणना:
यूक्लिड के विभाजन लेमा का प्रयोग करने पर,
117 = 65 × 1 + 52
⇒ 65 = 52 × 1 + 13
⇒ 52 = 13 × 4 + 0
∴ महत्तम समापवर्तक (65, 117) = 13
प्रश्न के अनुसार,
65m - 117 = 13
⇒ 65m = 117 + 13 = 130
⇒ m = 2
Last updated on Aug 9, 2024
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