integer in the units place of 63^63 is

M4maths Previous Puzzles

15 Feb 2011 unit\'s place

integer in the units place of 63^63 is

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10) 9

Solution

63*63*63*63 = ........1
so every pair of four 63 has 1 in unit's place.
Finally , we have three 63 and 63*63*63 = ......7
Hence the result

Correct Option: 8 Best Solution (7)

Shobin Thomas   13 years AGO

63^1=63, 63^2=..9, 63^3=...7, 63^4=....1, 63^5=.....3, and the cycle continues. Thus there are only 4 possibilites of the unit digit of 63^n. Considering the question, 63^63, we need to divide the exponent 63 by 4. We get quotitent of 15 and remainder of 3. The 3rd option among the possibilites, is a number ending with 7. Hence the correct answer is option 8, i.e. 7

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Neeraj Gupta   13 years AGO

we just divide the 63 by 4 because the cyclivity of 3 is 4...then we'll get the remender 3.
if remender is 1 then unit place=3
if remender is 2 then unit place=9
if remender is 3 then unit place=7
ant if remender is 0,unit place =1
hence ans will be 7 because remende is 3.

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atmakuri jagadish   13 years AGO

for units place ..........63^63 is nothing but 3^63..

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Mayank Maheshwari   13 years AGO

63^63 the cyclicity of 3 is 4 and when 63 is divided by 4 then the remainder is 3 so the unit place is 7 and our answer is option '8'

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A J V   13 years AGO

63^1=3, 63^2=9, 63^3=7, 63^4=1
similarly, 63^63=7.

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suneil   13 years AGO

63^63
divide 63 by 3. we get remainder as 3.
so 3^1=3, 3^2=9, 3^3=27
units place is 7

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Nishat Parveen   13 years AGO

63^1 has last digit 3
63^2 last digit 9
63^3 has last digit 7
63^4 has last digit 1
then the digits repeat after increment of every 4 nos in power.
now 63=15*4+3 means the last digit will be same as 3 which is 7.

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