Practice question · Numerical answer
Find the last digit of 7 raised to the power 4. (The last digit of a number is that number mod 10.)
Hints
- Work mod 10 and square in two stages rather than computing the whole power.
- 7 squared is 49, which is 9 mod 10; now square that.
Show the answer
1
Why
7 squared = 49 = 9 mod 10, and 9 squared = 81 = 1 mod 10, so the last digit is 1. (Indeed 7 to the fourth is 2401.) Reducing at every stage keeps the numbers to one digit, the technique that makes modular exponentiation practical even for the huge exponents used in cryptography.
Practise Modular Arithmetic
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