What is the tens digit of $6^{17}$ ?

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Official Explanation

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There are several ways to deal with this problem, some easier some harder, but almost all of them are based on pattern recognition.

The tens digit of 6 in integer power starting from 2 (

6^1

has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:

- The tens digit of

6^2 = 36

is 3.

- The tens digit of

6^3 = 216

is 1.

- The tens digit of

6^4 = ...96

is 9 (multiply 16 by 6 to get ...96 as the last two digits).…

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What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

What is the tens digit of 6176^{17}617?