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What is the last digit of 3^108?
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17 Mar 2022, 02:00
17 Mar 2022, 02:00
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What is the last digit of \(3^{108}\) ?
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GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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Great Opportunity To Earn Kudos!!!
GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
Re: What is the last digit of 3^108?
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17 Mar 2022, 11:46
17 Mar 2022, 11:46
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Cyclicity of 3 is 4 i.e. 3 *1 = 3 , 3*3 = 9, 3*3*3 = 27 and 3*3*3*3 = 81
So unit digit of 3 repeats after 4 cycles of 3,9,7 & 1
Now after dividing 108 by 4, we get 0 as reminder, so last digit of the expression should be 1
So unit digit of 3 repeats after 4 cycles of 3,9,7 & 1
Now after dividing 108 by 4, we get 0 as reminder, so last digit of the expression should be 1
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Re: What is the last digit of 3^108?
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13 Dec 2023, 08:17
13 Dec 2023, 08:17
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We need to find the units digit of \(3^{108}\)
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (108) by 4 and check what is the remainder
108 divided by 4 gives 0 remainder
=> Units digit of \(3^{108}\) = Units digit of \(3^4\) = 1
So, Answer will be 1
Hope it helps!
Watch this video to MASTER how to find Units digit of Power of 3
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (108) by 4 and check what is the remainder
108 divided by 4 gives 0 remainder
=> Units digit of \(3^{108}\) = Units digit of \(3^4\) = 1
So, Answer will be 1
Hope it helps!
Watch this video to MASTER how to find Units digit of Power of 3
