Question

2. Find the greatest number that will divide 55, 127
and 175, so as to leave the same remainder in each
case.


please solve this question..☺ ʕ•ﻌ•ʔ​

Answer 1

We can represent any integer number in the form of : pq + r , Where ' p ' is divisor, ' q ' is quotient , ' r ' is reminder.

So, we can write given numbers from given information , As :

55= p q1 + r --- ( 1 )

127 = p q2 + r --- ( 2 )

And

175 = p q3 + r --- ( 3 )

Here we want to find greatest value of ' p ' where remainder ' r ' is same , So

We subtract equation 1 from equation 2 we get :

p q2 - p q1 = 72 ,

p ( q2 - q1 ) = 72

And we subtract equation 2 from equation 3 we get :

p q3 - p q2 = 46 ,

p ( q3 - q2 ) = 46

And we subtract equation 1 from equation 3 we get :

p q3 - p q1 = 120 ,

p ( q3 - q1 ) = 120

Now to find greatest value of ' p ' we find H.C.F. of 72 , 46 and 120 , As :

72= 2×2×2×3×3 ,

46 = 2×23

And

120 = 2 × 2 × 3×3

So,

H.C.F. ( 72 , 46and 120 ) = 2

Therefore,

Greatest number that will divide 72 , 46 and 120 as to leave the same remainder in each case = 2 ( Ans )

Hope this information will clear your doubts about this question