So I guess we want to find N rite ??

 

So 770 = 2*5*7*11*1

 

Thus this is the only posititve solution ( here please note that i am assuming that the integeral solutions are distinct, otherwise (2,5,77,1,1) will also be a solution and so on)

 

Now there can be -ve integers as well ... However since 770 is positive only 2 or 4 out of 1,2,5,7,11 can be negative ...

 

So the total number of solutions will be 1 + ⁵C₂ + ⁵C₄ = 1 + 10 + 5  = 16

 

But please note the assmption that i have taken .... tell me if the answer is correct .. b'cos if the answer does not match then it means we cannot take that assumption. However i hope u have got the approach to solve the problem ..

 

cheers