SOLUTION: Find the units digit of 7^157.
Algebra.Com
Question 670006: Find the units digit of 7^157.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
To solve a question like this, one looks at of powers and a of .
.................unit's dig.
...............unit's dig.
..............unit's dig.
.............unit's dig. ...pattern:,,,
............
...........
...........
...........pattern is repeating
......
.....
.....
......pattern is repeating
So the unit's digits of powers of follow a cycle of length : ,,, ... ...
so let's find the remainder when we divide by :
Since the remainder is , and has the same unit's digit as , which is .
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