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Retired Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
How to Solve: Units' Digit of Power of 6
[#permalink]
20 Dec 2023, 20:24
20 Dec 2023, 20:24
1
Attachment:
How to Solve: Units' Digit of Power of 6
Hi All,
I have posted a video on YouTube to discuss Units' Digit of Power of 6
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
Theory of Units' Digit of Power of 6
- ⁍ Find Units’ digit of \(6^{71}\) ?
⁍ Find Units’ digit of \(6^{54}\) ?
⁍ Find Units’ digit of \(6^{70x + 41}\) (given that x is a positive integer)?
⁍ Find Units’ digit of \(2756^{205}\) ?
Theory of Units' Digit of Power of 6
• To find units' digit of any positive integer power of 6
| We need to find the cycle of units' digit of power of 6 | |
| \(6^1\) units’ digit is 6 | \(6^2\) units’ digit is 6 |
=> Units’ digit of any positive integer power of 6 = 6
Q1. Find Units’ digit of \(6^{71}\)?
Show: ::
Sol: Since 71 is a positive integer
=> Units' digit of \(6^{71}\) = 6
=> Units' digit of \(6^{71}\) = 6
Q2. Find Units’ digit of \(6^{54}\)?
Show: ::
Sol: Since 54 is a positive integer
=> Units' digit of \(6^{54}\) = 6
=> Units' digit of \(6^{54}\) = 6
Q3. Find Units’ digit of \(6^{70x + 41}\) (given that x is a positive integer)?
Show: ::
Sol: Since 70x + 41 is a positive integer
=> Units' digit of \(6^{70x + 41}\) = 6
=> Units' digit of \(6^{70x + 41}\) = 6
Q4. Find Units’ digit of \(2756^{205}\) ?
Show: ::
Sol: Units' digit of power of any number = Units' digit of power of the units' digit of that number
=> Units’ digit of \(2756^{205}\) = Units’ digit of \(6^{205}\)
Since 199 is a positive integer
=> Units' digit of \(2756^{205}\) = 6
=> Units’ digit of \(2756^{205}\) = Units’ digit of \(6^{205}\)
Since 199 is a positive integer
=> Units' digit of \(2756^{205}\) = 6
Master List of Units' Digit of Power of Numbers from 2 to 9
Hope it helps!
gmatclubot
How to Solve: Units' Digit of Power of 6 [#permalink]
20 Dec 2023, 20:24
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