Question

The remainder when 3^256 is divided by 100

Answer 1

Answer:

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Answer 2

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$\implies$Well, if we are dividing by 5, then it is only necessary to find the units digit of 3²⁵⁶

If we find a pattern,

3¹ = 3

3² = 9

3³ = 27, last digit is 7

3⁴ = 81, last digit is 1

3⁵ = 243..

So therefore, each 4th power of 3 ends with a units digit of 1. So therefore, 3²⁵⁶ ends with a units digit of one. And when dividing such a number by five (e.g. 11, 21, 31), the remainder is always 1.

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