Q. 183.9( 15 Votes )

Find the greatest

Answer :

Given: The numbers 285 and 1249.


To find: The greatest number which leaves remainder 9 and 7 in 285 and 1249.


Concept Used:


Euclid's division lemma:


If there are two positive integers a and b,


then there exist unique integers q and r such that,


a = bq + r where 0 ≤ r ≤ b.


Explanation:


The new numbers after subtracting remainders are:


285-9 = 276


1249-7 = 1242


The required number = HCF of 276 and 1242


Let a = 1242 and b = 276


As 1242>276


By applying Euclid’s division lemma,


1242 = 276q + r, (0≤r<276)


On dividing 1242 we get quotient as 4 and remainder r as 138.


1242 = 276× 4 + 138


Now apply Euclid’s division lemma on 276 and 138,


276 = 138q+ r, (0≤r<138)


On dividing 276 we get quotient as 2 and remainder r as 0.


276 = 138 × 2 + 0


HCF = 138


Hence remainder is = 0


Hence required number is 138


Hence the greatest number which divides 285 and 1249 leaving remainder 9 and 7 respectively is 138.


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