Question

What is last digit of $17^{456}$

Answer 1

the last digit of $17^{456}$ is 1
$17^1=17,17^2=289,17^3=4913,17^4=83521,17^5=1419857..$
so u can see last digits are coming in series
so as 456 is a multiple of 4
it has last digit 1
as $17^8=6975757441,17^{12}=582622237229761$

Answer 2

if u consider  7^1  the last digit is 7     if u consider   7^2   the last digit is 4     and so on



u will soon .       456  is the multiple of  3   and 4      therefore   hcf of 3 and 4 is 1
therefore we will consider   7^1
and hence the last digit is 7