Question

what is the reminder when 3 to the power of 2019 is divided by 5

Answer 1

2 is the remainder...

Answer 2

Answer:

Remainder = 2

Step-by-step explanation:

$3^1 = 3\\\\3^2 = 9\\\\3^3 = 27\\\\3^4 = 81\\\\3^5 = 243........$

For any power of 3 unit digits would be 1, 3,7,or 9. Also if you notice, after every 4th power of 3, the unit digit would repeat itself.  

Therefore, in the question :

$3^{2019}\text{ (or }3^{2016 + 3})\textbf{ would have unit digit of 7}$

Hence, a number whose unit digit is 7 and divided by 5, it will give remainder 2.