Problem solving with programming: Last digit of a power
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Given a number expressed in base, exponent form (ab) where a is arbitrary big number For example contains 100 digits, We have to write a program to find the last digit in it's expanded form.
Eg: 45712 has a last digit of 1
We have to observe that the powers of single digit repeat after if we go on increasing the exponent.
Look at the following table. It gives a fair idea of our approach.
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 2 | 2 | 4 | 8 | 6 |
| 3 | 3 | 9 | 7 | 1 |
| 4 | 4 | 6 | 4 | 6 |
| 5 | 5 | 5 | 5 | 5 |
| 6 | 6 | 6 | 6 | 6 |
| 7 | 7 | 9 | 3 | 1 |
| 8 | 8 | 4 | 2 | 6 |
| 9 | 9 | 1 | 9 | 1 |
The the last digit in the power of 2 repeats every multiple of 4. Similarly the last digit in powers of 4 repeats every multiple of 2. and so on.
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