Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Question

If 'P' is the greatest number, that divides 9086, 12326 and 23126 leaving the same remainder in each case.
What is the sum of digits in P?

Answer 1

The answer is 4

Lets put them into equations
43 = D*q1 + r1;
91 = D*q2 + r2;
183 = D*q3 + r3;

and r1=r2=r3=r

so.
D*(q2-q1)= 48
D*(q3-q2)= 92
D*(q3-q1)= 140

For the greatest value of D take the HCF of 48, 92 and 140 which is 4.

Answer 2

1
the remainder in each case is 0!