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?

Answer 1

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