Try to answer the following:
What is the units digit (last digit) of 22011 ?
THE MAGIC REMAINDER TECHNIQUE
(For numbers with a very large exponents)
To get the last digit of a number with a very large exponent:
Step 1. Get last 2 digits of the exponent.
Step 2. Divide by 4 and get remainder.
Step 3. The remainder becomes the new exponent.
- What is the units digit (last digit) of 22011 ?
Step 1. 22011 –> 211
Step 2. Divide 11 by 4. Remainder = 3
Step 3. 211 –> 23 = 8
Answer: Last digit = 8
Exception to the Rule: If the remainder is zero, exponent should be 4, not 0.
Example: 312 –> 34 = 81. Last digit = 1.
NOW, IT’S YOUR TURN!
- What is the units digit of 32014 ?
- What is the units digit of 7326 ?
- What is the units digit of 9878 ?
- What is the units digit of 62015 ?
- CHALLENGE: What is the units digit of 1232014 ?
Reflection for the Pro (if you are BRAVE enough!)
- If the base has more than one digit, what shortcut can you suggest?
- Think of a faster way if the base is 4 or 9. What if the base is 1, 5, 6 or 0?
–Wacks Formula 🙂
Disclaimer: The name of the formula is purely for fun, and does not discredit others who might have discovered the same formula independently.