Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

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134

136

138

132

answer is B.

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Detailed Solution

The given integers are 285 and 1249.
As per Euclid’s Division Lemma, if there are two positive integers a and b, then there exist unique q and r such that they satisfy the condition:

a = bq + r

where

0 \leq r < b

Subtract the remainders 9 and 7 from 285 and 1249. That is,

285 - 9 = 276

1249 - 7 = 1242

Calculation of HCF of 276 and 1242 using Euclid’s division algorithm is as follows:

1242 = 276 \times 4 + 138

276 = 138 \times 2 + 0

So, the HCF of 276 and 1242 is 138.
Therefore, 138 is the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
Hence, option 2 is correct.

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