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यदि 408 तथा 1032 के HCF को 1032m – 408 × 5 के रूप में प्रकट किया जाता है तो m का मान ज्ञात कीजिए।

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यदि 408 तथा 1032 के HCF को 1032m – 408 × 5 के रूप में प्रकट किया जाता है तो m का मान ज्ञात कीजिए।

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यूक्लिड विभाजन प्रमेयिका से,

1032 = 408 × 2 + 216

408 = 216 × 1 + 192

216 = 192 × 1 + 24

192 = 24 × 8 + 0

अत: HCF (408, 1032) = 24

दिया है, 24 = 1032m – 408x × 5

⇒ 24 + 2040 = 1032m

⇒ 2064 = 1032m

m = 2064/1032 = 2

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