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प्रश्न
Find the largest number which divides 546 and 764, leaving remainders 6 and 8 respectively.
संख्यात्मक
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उत्तर
Given: Numbers 546 and 764 leave remainders 6 and 8 respectively.
Subtract the remainders: 546 – 6 = 540 and 764 – 8 = 756.
The required largest divisor is the HCF (gcd) of 540 and 756.
Compute gcd(540, 756) by the Euclidean algorithm:
756 = 540 × 1 + 216
540 = 216 × 2 + 108
216 = 108 × 2 + 0
So, gcd = 108.
The largest number is 108.
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