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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1131
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 5
[#permalink]
20 Dec 2023, 07:14
20 Dec 2023, 07:14
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How to Solve: Units' Digit of Power of 5
Hi All,
I have posted a video on YouTube to discuss Units' Digit of Power of 5
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 5
- ⁍ Find Units’ digit of \(5^{61}\) ?
⁍ Find Units’ digit of \(5^{33}\) ?
⁍ Find Units’ digit of \(5^{79x + 31}\) (given that x is a positive integer)?
⁍ Find Units’ digit of \(1055^{199}\) ?
Theory of Units' Digit of Power of 5
• To find units' digit of any positive integer power of 5
| We need to find the cycle of units' digit of power of 5 | |
| \(5^1\) units’ digit is 5 | \(5^2\) units’ digit is 5 |
=> Units’ digit of any positive integer power of 5 = 5
Q1. Find Units’ digit of \(5^{61}\)?
Show: ::
Sol: Since 61 is a positive integer
=> Units' digit of \(5^{61}\) = 5
=> Units' digit of \(5^{61}\) = 5
Q2. Find Units’ digit of \(5^{33}\)?
Show: ::
Sol: Since 33 is a positive integer
=> Units' digit of \(5^{33}\) = 5
=> Units' digit of \(5^{33}\) = 5
Q3. Find Units’ digit of \(5^{79x + 31}\) (given that x is a positive integer)?
Show: ::
Sol: Since 79x + 31 is a positive integer
=> Units' digit of \(5^{79x + 31}\) = 5
=> Units' digit of \(5^{79x + 31}\) = 5
Q4. Find Units’ digit of \(1055^{199}\) ?
Show: ::
Sol: Units' digit of power of any number = Units' digit of power of the units' digit of that number
=> Units’ digit of \(1055^{199}\) = Units’ digit of \(5^{199}\)
Since 199 is a positive integer
=> Units' digit of \(1055^{199}\) = 5
=> Units’ digit of \(1055^{199}\) = Units’ digit of \(5^{199}\)
Since 199 is a positive integer
=> Units' digit of \(1055^{199}\) = 5
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 5 [#permalink]
20 Dec 2023, 07:14
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