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Q.

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

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a

134

b

136

c

138

d

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≤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=276×4+138 276=138×2+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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