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Q.

Find the greatest number which divides , and exactly leaving remainders , and respectively.

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a

b

c

d

None of these

answer is C.

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Detailed Solution

Concept: Subtract the remainder terms from each number and find the highest common factor of all the required numbers by prime factorisation method. Here, the highest common factor is basically the greatest number which can divide the whole number properly.
Given numbers are

,

,

and they are leaving the remainders

,

,

respectively.
Subtract the remainders from the numbers,
Required numbers are

By prime factorisation method, factors of the following are;

It implies that,

Therefore,

is the greatest number which divides

,

and

exactly leaving remainders

,

and

.
Hence, the correct answer is option (3).

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