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Bunuel
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What is the units digit of 7^94? 13 Jul 2021, 03:00
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E
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5% (low)

Question Stats:

80% (00:40) correct 20% (01:04) wrong based on 195 sessions

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What is the units digit of 7^94?

A. 1
B. 3
C. 5
D. 7
E. 9
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E
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rajatchopra1994
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What is the units digit of 7^94? 13 Jul 2021, 03:04
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Explanation:

7^94

Cyclicity of 7 is : 7,9,3,1

Divide 94 by 4 , remainder is cyclicity no.
Here remainder is 2
Unit digit will be 9.

IMO-E

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What is the units digit of 7^94? 13 Jul 2021, 03:10
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Cyclicity of 7 is 4 ...i.e 7, 9, 3,1
94 mod 7 is 2
Units digit of 7^94 will be 9 i.e Option E is correct

Bunuel
What is the units digit of 7^94?

A. 1
B. 3
C. 5
D. 7
E. 9
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What is the units digit of 7^94? 03 Oct 2024, 07:33
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What is the units digit of 7^94?

Now to find the unit's digit of \(7^{94}\), we need to find the pattern / cycle of unit's digit of power of 7 and then generalizing it.

Unit's digit of \(7^1\) = 7
Unit's digit of \(7^2\) = 9
Unit's digit of \(7^3\) = 3
Unit's digit of \(7^4\) = 1
Unit's digit of \(7^5\) = 7

So, unit's digit of power of 7 repeats after every \(4^{th}\) number.
=> We need to divided 94 by 4 and check what is the remainder
=> 94 divided by 4 gives 2 remainder

=> \(7^{94}\) will have the same unit's digit as \(7^2\)
=> Unit's digits of \(7^{94}\) = 9

So, Answer will be E
Hope it helps!

Link to Theory for Last Two digits of exponents here.

Link to Theory for Units' digit of exponents here.
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Bunuel
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