Can you find out the remainder when 3^300 is divided by 5?

3

3 It is obvious that it is not feasible to calculate 3^300 as it will take too much of time. So we will use a trick to solve the question. We will calculate the remainder of each power till we find a pattern. 3^1 divided by 5 leaves the remainder 3. 3^2 divided by 5 leaves the remainder 4. 3^3 divided by 5 leaves the remainder 2. 3^4 divided by 5 leaves the remainder 1. 3^5 divided by 5 leaves the remainder 3. 3^6 divided by 5 leaves the remainder 4. As you can see that the pattern is now repeating itself and it will go on like this till 3^300 and beyond. Since every fourth remainder is same as the first, we will look for the power of 4 only. 300 is divisible by 4. Therefore at the power of 300, the first remainder will repeat itself and the remainder will be 3.