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Question

In the question let Me be the greatest no that will divide 1305,4665,6905 with same remainder in each case, why do we subtract the numbers from each other?


Solution

Upto my understanding 
(4665 - 1305)=3360, (6905 - 4665)=2240 and (6905 - 1305)=5600
3360:2240:5600
1120:1120:1120


Let the numbers be represented as 

1305 = Na + d  ---------------------(1)

where q is the remainder 

Also , 

4665 = Nb + d  ---------------------(2)

6905 = Nc + d  ---------------------(3)

Subtracting eq(1) from eq(2) we get

Nb - Na = 3360

N(b-a) = 3360  

for N to be maximum (b-a) is to be minimum

Also , subtracting eq(1) from eq(3) we get

Nc - Na = 5600

N(c-a) = 5600

Also subtracting eq(2) from eq(3) we get

Nc - Nb = 2240

N(c-a) = 2240

Now we need to find HCF of (3360 , 5600 , 2240)  , that is 80 which is equal to value of N

Thus N is 1120

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