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Units Digit

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by stop@800 » Mon Oct 27, 2008 1:08 pm
Is answer 1 ??


(13^4)(17^2)(29^3)


unit digit
(13^4) : 1
(17^2) : 9
(29^3) : 9

Overall 9*9 : 1
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by EricLien9122 » Mon Oct 27, 2008 1:12 pm
3x3x3x3=....1.
7*7*1=....9.
9*9*9*9=....1

Hence, answer is 1.
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by vishubn » Mon Oct 27, 2008 5:56 pm
On the same line !
its same as finding the unit digits of 3,7,9 multiples

p.s. should know the repeating sequence of these powers

so it is

1*9*9=81 unit digit is 1

IMO=1

vishu
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by piyushdabomb » Mon Oct 27, 2008 8:45 pm
I don't understand. Can someone explain this in more detail? Why are you only looking at the units digits of the individual numbers 13, 17, and 29?

Explanation required. How would you do this problem exactly?


what if I said instead of 13^4, I said 130? What changes...
(13^4)(17^2)(29^3)?
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by vishubn » Mon Oct 27, 2008 10:07 pm
First and foremost:

(13^4)---- 13*13*13*13 this gives any idea that we need to be bothered about 3 powers

unit digits of powers of 3 is 3,9,7,1,3,9,7,1 repeating sequence

so we know now the number will be with the digit 1

(17^2)
and same heer as well ! 17*17= some number with unit digit 9


(29^3)
same logic 29*29*29= where 9 has a repating sequence of 9,1,9,1
now the number formed will have a unit digit 9

so question is to find the unit digit of the above multiples :

9*9*1=81 and unit digit of this number is 1

key to this problem is to be aware of all repeating sequence of the power ! do work it out ! every number raised to power has a sequence of its own

Vishu
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by piyushdabomb » Tue Oct 28, 2008 5:07 am
Vishnu,

Hold on here - still a little confusing....

Lets start with the repeating sequence of 3. Why does the units HAVE to be 1 just because it is the last repeating sequence number? Why can't the units digit be 1, 3, 9, etc...?

Why did you multiply all the units at the end? How does multiplying give you more units?

I'm sorry...still just dont really see it.
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by sudhir3127 » Tue Oct 28, 2008 5:34 am
piyushdabomb wrote:Vishnu,

Hold on here - still a little confusing....

Lets start with the repeating sequence of 3. Why does the units HAVE to be 1 just because it is the last repeating sequence number? Why can't the units digit be 1, 3, 9, etc...?

Why did you multiply all the units at the end? How does multiplying give you more units?

I'm sorry...still just dont really see it.
i think u need to be a bit more familiar with numbers cyclicity...

why we say that the units digit is 1 when its 3^4 is
3^1 = units digit is 3
3^2 = units is 9
3^3 = units is 7 ( 3^3 = 27)
3^4 = units is 1 ( 3^4 = 81)
3^5 = 3 ( 3^5= 243)

so if u study the trend carefully ... it repeats after every power of 4.

hence 13^4 can be written as 3^4 = 1
take the example of 3^13

it can be written as 3^1 = 3 ( 13/ 4 = 3 and remainder as 1)

Hope its makes more sense now..

do let me know if u need any more help on this ...
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by vishubn » Tue Oct 28, 2008 6:24 am
Yaaa !
Sudhir did answer the question !
Okay please if u still in doubt !
let break up ! and u ask wat point u have doubt ! and we will try pitching in ideas :)

vishu
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by selango » Thu Aug 05, 2010 8:32 am
13^15

13^1=3

13^2=9

13^3=7

13^4=1

13^5=3

13^15=13^12*13^3=(13^4)^3 * 13^3=1*7=7

Units digit of 13^15=7
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by Abhishek009 » Thu Aug 05, 2010 8:53 am
gmathope wrote:Sorry folks, I am still not sure how to quickly calculate the units digit in this case? 13^15

Any help would be great.
Already sudhir and others have given good explanation , so I would not exaggerate it .

Plz visit the following link https://takshzilabeta.com/index.php?opti ... -&Itemid=5

In case of any doubt feel free to ask any question.
Abhishek
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by gmatmachoman » Fri Aug 06, 2010 5:53 am
selango wrote:13^15

13^1=3

13^2=9

13^3=7

13^4=1

13^5=3

Now u can see that "pattern/cyclicity" is formed. After every 4 numbers the unit digit repeats itself.

So Remainder (15/4) = 3

So unit digit of raised to the power 3 will be same as raised to power 15.

Units digit of 13^15=7
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