What are the last three digits of the number 7^411? How would I go about solving this? Thanks!
+128474 Note that 7^11 ends in 743
And 7^100 ends in 001
And 7^200 ends in 001 because we would be multiplying (7^100) x (7^100) which would have the following result in the last 3 digits......
........001
x ........001
-----------------
..........001
........ 00
.........0
----------------
.............001
So.....7^400 would also end in 001 because we would be squaring 7^200 = (.......001) x (........001) which would have the same three ending digits as above
Therefore 7^411 = 7^200 x 7^200 x 7^11 would end in
.................001
.................743
------------------
.........003
.........04
.........7
--------------------
.................743
And 743 is the answer.....!!!
+128474 Note that 7^11 ends in 743
And 7^100 ends in 001
And 7^200 ends in 001 because we would be multiplying (7^100) x (7^100) which would have the following result in the last 3 digits......
........001
x ........001
-----------------
..........001
........ 00
.........0
----------------
.............001
So.....7^400 would also end in 001 because we would be squaring 7^200 = (.......001) x (........001) which would have the same three ending digits as above
Therefore 7^411 = 7^200 x 7^200 x 7^11 would end in
.................001
.................743
------------------
.........003
.........04
.........7
--------------------
.................743
And 743 is the answer.....!!!
