Question

When 4^500! - 6¹⁶¹ is divided by 7. What is the remainder?

Answer 1

Correct Answer - Option 2 : 2

Calculation:

4^500! Can be written as 64^4k

⇒ 64 divided by 7 gives remainder = 1

Hence, 4^500! Divided by 7 gives 1 as the remainder

⇒ Using remainder properties 6¹⁶¹ = (-1)¹⁶¹

⇒  6¹⁶¹/7 = 6 (Remainder)

Hence, 4^500! - 6¹⁶¹ divided by 7 will be -5 i.e 7 - 5 = 2 (By remainder theorem)

∴ Required remainder will be 2