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Q.

Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively.

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a

2 and 5 

b

4 and 3

c

7 and 2

d

3 and 2

answer is B.

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Detailed Solution

We have to find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively.
Euclid's Division Lemma states that, if two positive integers “a” and “b”, then there exists unique integers “q” and “r” such that which satisfies the condition:
a=bq+r where 0≤r≤b
Subtract the remainder 4 and 3 from 280 and1245.
280-4=276
1245-3=1242
Calculation of HCF using Euclid’s division algorithm is as follows:
Question ImageQuestion Image⇒HCF(276,1242)=138
Therefore, 138 is the greatest number which divides 280 and 1245 leaving remainders 4 and 3 respectively.
Hence, option 2 is correct.
 
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