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Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
How to Solve: Units' Digit of Power of 4
[#permalink]
18 Dec 2023, 04:58
18 Dec 2023, 04:58
1
Attachment:
How to Solve: Units' Digit of Power of 4
Hi All,
I have posted a video on YouTube to discuss Units' Digit of Power of 4
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 4
- ⁍ Find Units’ digit of \(4^{51}\) ?
⁍ Find Units’ digit of \(4^{33}\) ?
⁍ Find Units’ digit of \(4^{44}\) ?
⁍ Find Units’ digit of \(4^{60x + 61}\) (given that x is a positive integer)?
⁍ Find Units’ digit of \(12954^{1053}\) ?
Theory of Units' Digit of Power of 4
• To find units' digit of any positive integer power of 4
| We need to find the cycle of units' digit of power of 4 | |
| \(4^1\) units’ digit is 4 \(4^2\) units’ digit is 6 | \(4^3\) units’ digit is 4 \(4^4\) units’ digit is 6 |
=> The power repeats after every \(2^{nd}\) power
=> Cycle of units' digit of power of 4 = 2
=> Units' digit of odd power of 4 = 4
=> Units' digit of even power of 4 = 6
Q1. Find Units’ digit of \(4^{51}\)?
Show: ::
Sol: 51 is Odd
=> Units' digit of \(4^{51}\) = 4
=> Units' digit of \(4^{51}\) = 4
Q2. Find Units’ digit of \(4^{33}\)?
Show: ::
Sol: 33 is Odd
=> Units' digit of \(4^{33}\) = 4
=> Units' digit of \(4^{33}\) = 4
Q3. Find Units’ digit of \(4^{44}\)?
Show: ::
Sol: 44 is Even
=> Units' digit of \(4^{Even}\) = 6
=> Units' digit of \(4^{Even}\) = 6
Q4. Find Units’ digit of \(4^{60x + 61}\) (given that x is a positive integer)?
Show: ::
Sol: 60x + 61 = Even + Odd = Odd
=> Units' digit of \(4^{60x + 61}\) = 4
=> Units' digit of \(4^{60x + 61}\) = 4
Q5. Find Units’ digit of \(12954^{1053}\) ?
Show: ::
Sol: Units' digit of power of any number = Units' digit of power of the units' digit of that number
=> Units’ digit of \(12954^{1053}\) = Units’ digit of \(4^{1053}\)
=> 1053 is Odd
=> Units' digit of \(12954^{1053}\) = Units, digit of \(4^{1053}\)= 4
=> Units’ digit of \(12954^{1053}\) = Units’ digit of \(4^{1053}\)
=> 1053 is Odd
=> Units' digit of \(12954^{1053}\) = Units, digit of \(4^{1053}\)= 4
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 4 [#permalink]
18 Dec 2023, 04:58
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