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Q.

Find the greatest number which divides 399, 434 & 537 leaving the remainder 8, 9 & 10 respectively.


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a

17

b

18

c

19

d

11 

answer is A.

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Detailed Solution

The number divides 399, 434 and 537 leaving the remainder 8, 9 and 10.
So, that number will divide (399−8), (434−9) and (537−10) completely.
Now, the greatest number that will divide 391,425 and 527 completely, is the H.C.F. of these numbers.
391 = 17 × 23
425 =5 × 5 × 17
527 = 17 × 31
H.C.F. =17
 
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