Question

find the greatest number which divides 107 and 185 leaving the remaining 2 and 5 respectively

Answer 1

It's simple....
First subtract 2 and 5 respectively.....

Then follow the normal procedure of finding the HCF( highest common factor )....

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Answer 2

Hey friend, Harish here.

Here is your answer:

Let the greatest number be 'x'.

Given that,

When x divides 107 and 185 it leaves a remainder 2 & 5 respectively . 

Now,
107 - 2 = 105. 
 
185 - 5 = 180

So, x divides 105 & 180 perfectly leaving no remainder. 

Then x  is equal to the HCF of 105 & 180.

So, HCF( 105, 180 ) is :

180 = 105 × 1 + 75 

105 = 75 × 1 + 30
 
75 = 30 × 2 + 15
 
30 = 15 × 2 + 0.

15 is the HCF of the number. So, x is 15.

Therefore 15 is the greatest number which divides 107 & 185 leaving remainders 2 & 5 respectively. 
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Hope my answer is helpful to you.