#1**+5 **

Notice the pattern generated by raising a number ending in 7 to the following powers.....

7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401

And this cyclic pattern repeats every four powers

So ... 256/4 = 64

And this whole number tells us that 7^256 completes a cycle of 4, so this number ends in a "1"

CPhill
Feb 21, 2015

#1**+5 **

Best Answer

Notice the pattern generated by raising a number ending in 7 to the following powers.....

7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401

And this cyclic pattern repeats every four powers

So ... 256/4 = 64

And this whole number tells us that 7^256 completes a cycle of 4, so this number ends in a "1"

CPhill
Feb 21, 2015