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What is the units digit of 3^66?

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What is the units digit of 3^66?

by Max@Math Revolution » Sun Jul 03, 2016 4:35 pm
What is the units digit of 3^66?
A. 1
B. 3
C. 5
D. 7
E. 9

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by 800_or_bust » Sun Jul 03, 2016 4:42 pm
Max@Math Revolution wrote:What is the units digit of 3^66?
A. 1
B. 3
C. 5
D. 7
E. 9

*An answer will be posted in 2 days
Look for a pattern...

3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3 (REPEATS HERE)

1+4n:3

n=16, then 1+4(16) = 65.

So 3^65 = 3.

And 3^66 = 9.

Answer choice: E.
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by Max@Math Revolution » Tue Jul 05, 2016 8:05 pm
From 3^1=3, 3^2=9, 3^3=27, 3^4=81, the unit digit repeats in 3-->9-->7-->1-->3. Then, from 3^66=3^(4(16)+2), the unit digt is same as that of ^2. Hence, the answer is 9 and the correct answer choice is E.
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