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.Solution
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
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