Question

If (1728²⁶ - 2¹⁵⁶) is divided by 16, what will be the remainder?

Answer 1

Correct Answer - Option 1 : 0

Given:

Dividend = (172826 - 2156)

Divisor = 16

Concept Used:

Dividend = (divisor × quotient) + remainder 

Calculation:

(172826 - 2156) = (12^3×(26) - 2¹⁵⁶)/2⁴

⇒ (123×(26) - 2156)/24 = (2^{(6 × 26)} × 3^{(3 × 26)} - 2¹⁵⁶) /2⁴

⇒ (2(6 × 26) × 3(3 × 26) - 2156) /24 = 2¹⁵⁶(3⁷⁸ - 1)/2⁴

⇒ 2156(378 - 1)/24 = 2^{(156 -4)}(3⁷⁸ - 1) = 2(152)(378 - 1)

The divisor 16 completely divides the number (172826 - 2156), so remainder is 0

∴ (172826 - 2156) is divided by 16, the remainder is 0