Question

Let x represent the largest number that can divide the numbers 603, 1698, and 1041, leaving the same remainder in each case. Calculate the value of 2x−r+5, where r is the common remainder.

Q: Answer-Let x represent the largest number that can divide the numbers 603, 1698, and 1041, leaving the same...

Let the number which divides 603, 1698 and 1041 be x and the remainder be r. Hence, x divides 603 r, 1698 r and 1041 r. Then, x divides 1698 - r 1041 - r and x divides 1041 - r 603 - r x divides 657 and x divides 438. Hence, H.C.F of 657 and 438 219 r 603 219 2 603 438 165 Therefore, 2x r 5 2 219 - 165 5 278