JMO

If 23⁵⁶ is divided by 11 what is the Remainder?

Answer:

23⁵⁶ = (11 + 12)⁵⁶ = 11⁵⁶ + 56.11⁵⁵.12…… + 56.11.12⁵⁵ + 12⁵⁶

Now, 23⁵⁶/11 = [11⁵⁶ + 56.11⁵⁵.12…… + 56.11.12⁵⁵ + 12⁵⁶] / 11

All the terms are divisible by 11 except 12⁵⁶

Now, 12 ⁵⁶ = (11 + 1)⁵⁶ = [11⁵⁶ + 56.11⁵⁵.1…… + 56.11.1⁵⁵ + 1⁵⁶]

All the terms are divisible by 11 except the last term, i.e. 1⁵⁶ = 1

So, 12⁵⁶/11 has Remainder = 1

So, answer is 1.