Here we will show you how to find the last digit of any number with a large Exponent. In other words, if we calculate the number and get the result called the Power, then what is the last digit of the Power?
BaseExponent = Power
Here are all the different scenarios and how to find the last digit of the Power. It really all depends on the last digit of the Base.
0 Last digit of the Power if the last digit of the Base number is 0
The last digit of the Power will always be 0 regardless of what the Exponent is.
1 Last digit of the Power if the last digit of the Base number is 1
The last digit of the Power will always be 1 regardless of what the Exponent is.
2 Last digit of the Power if the last digit of the Base number is 2
First divide the Exponent by 4. The fractional part of the quotient will either be 00, 25, 50, or 75. The last digit of the Power is accordingly:
00 = last digit of the Power 6
25 = last digit of the Power 2
50 = last digit of the Power 4
75 = last digit of the Power 8
3 Last digit of the Power if the last digit of the Base number is 3
First divide the Exponent by 4. The fractional part of the quotient will either be 00, 25, 50, or 75. The last digit of the Power is accordingly:
00 = last digit of the Power 1
25 = last digit of the Power 3
50 = last digit of the Power 9
75 = last digit of the Power 7
4 Last digit of the Power if the last digit of the Base number is 4
If the Exponent is odd, then the last digit of the Power is 4. If the Exponent is even, then the last digit of the Power is 6.
5 Last digit of the Power if the last digit of the Base number is 5
The last digit of the Power will always be 5 regardless of what the Exponent is.
6 Last digit of the Power if the last digit of the Base number is 6
The last digit of the Power will always be 6 regardless of what the Exponent is.
7 Last digit of the Power if the last digit of the Base number is 7
First divide the Exponent by 4. The fractional part of the quotient will either be 00, 25, 50, or 75. The last digit of the Power is accordingly:
00 = last digit of the Power 1
25 = last digit of the Power 7
50 = last digit of the Power 9
75 = last digit of the Power 3
8 Last digit of the Power if the last digit of the Base number is 8
First divide the Exponent by 4. The fractional part of the quotient will either be 00, 25, 50, or 75. The last digit of the Power is accordingly:
00 = last digit of the Power 6
25 = last digit of the Power 8
50 = last digit of the Power 4
75 = last digit of the Power 2
9 Last digit of the Power if the last digit of the Base number is 9
If the Exponent is odd, then the last digit of the Power is 9. If the Exponent is even, then the last digit of the Power is 1.
Here are some examples using our instructions on this page:
Last digit of 12345^1234
Answer is 5 because last digit of Base is 5.
Last digit of 1273^122
Last digit of Base is 3 and 122/4 = 30.50. Thus, answer is 9.
Last digit of 1234^33
Last digit of Base is 4 and Base is odd. Thus, answer is 4.
Check out these tools related to numbers with large Exponents:
Cyclicity Calculator
Calculate the Cyclicity of any number.
Last Digit Calculator
Don't have time to learn all the rules on this page? Then use this calculator to find the answer fast.