The remainder when ((6^6)^6)^6… is divided by 10 is

Question

GMATBusters’ Quant Quiz 2.0 Question -2 
 For questions from previous quizzes click   here

The remainder when ((6^6)^6)^6… is divided by 10 is 
A. 2
B. 3
C. 4
D. 5
E. 6

willacethis · Answer

This can be written as 6^(6*6*6....*6).

Now, any number that ends with 6 will always have 6 in units place for all positive powers.

Since the aforementioned number has 6 in units place, it will have remainder of 6 when divided by 10.

Hence, answer = E

rvarora · Answer

Because the cyclicity of 6 is 1
Number 6 raised to any integer power will always have its units digit as 6
and hence when divided by 10 will always yield remainder 6

Answer: E

numb007 · Answer

Ans;E
SInce the last digit of the expression ((6^6)^6)^6 will always be 6. When the result will be divided by 10,the reminder will be 6.

pk123 · Answer

The remainder when ((6^6)^6)^6… is divided by 10 is
A. 2
B. 3
C. 4
D. 5
E. 6

6 raise to power of any number gives 6 as unit's digit
ex. 6^2=36, 6^3=216, 6^4=1296, 6^5=7776 and 6^6=46656

Hence if the term is divided by 10, answer will be 6 (Option E)

gvij2017 · Answer

Reminder after dividing 10 means unit digit.

If unit digit of n is 6 then any power of n will give unit digit 6. 
E is answer.

globaldesi · Answer

6 raised to any positive integer will always have a unit digit as 6
and a number of form abcd....6 when divided by 10 will leave 6 as remainder
thus 6 is the remainder hence E

Jawad001 · Answer

Unit digit of six to the power any value results in 6
So, six to the power of 6 divided by 10 is equal to 6

Answer:6(E)

fauji · Answer

Approach

Formula : If a number is divided by 10, its remainder is the last digit of that number.

In this Case:  ((6^6)^6)^6  is divided by 10
Notice that any power of 6 will result in a number with Unit digit as '6'
For e.g.  6^2  = 36,  6^3  = 216 ....  6^6  = 46656

So in this case when divided by 10, remainder is 6

Option E

QuantMadeEasy · Answer

Unit digit of ((6^6)^6)^6… is 6 
therefore when ((6^6)^6)^6… is divided by 10, the remainder will be 6

IMO E

lacktutor · Answer

The remainder when ((6^6)^6)^6… is divided by 10 is ????

No matter what positive integer is the power of 6, the units digit of that number always will end with 6.
--> that's why, when  ((6^{6})^{6})^{6} … is divided by 10, the remainder will be 6.

The answer is E.

SUNNYRHODE002 · Answer

Solution :

This Number will always end in "6" as its unit digit.

Therefore, Remainder by 10 indirectly asks us to find out the Unit's Digit of the number.
 
Answer: 6

vishumangal · Answer

Reminder when 6^6 is divided by 10 is 6
Thus no matter how much we raise the power with 6 remainder will still remain 6 Only

Archit3110 · Answer

remainder when 
6^1 = 6
6^2 = 6
6^3= 6
so for all multiple values for 6^x divided by 10 will give remainder = 6
IMO E: 6

The remainder when ((6^6)^6)^6… is divided by 10 is
A. 2
B. 3
C. 4
D. 5
E. 6

Raxit85 · Answer

6^0 = 1, 6^1 =6, 6^2=36, 6^3=216, 6^4 = ...6, 6^5 = .......6, 6^6 = ......6 
So, the unit digit ends in 6 from power 1 to infinity.
According to PEMDAS, 
((6^6)^6)^6…
((.....6)^6)^6...
(..........6)^6...
(...............6) to infinity
The last digit will be 6 only. So, by dividing the number with 10, the remainder will be 6 only.

Hence. Ans. is E.

Aviral1995 · Answer

Since 6 raise to any power greater than 0 leaves the unit digit as 6
therefore when the given value in question is divided by 6--> answer is 6

mohagar · Answer

E is the correct option

hiranmay · Answer

The remainder when ((6^6)^6)^6… is divided by 10 is
A. 2
B. 3
C. 4
D. 5
E. 6-->  correct

Solution :
6^1 = 10*0+6 --> reminder is 6
6^2 = 36 = 10*3+6 --> reminder is 6
6^3=216 = 10*210+6 --> reminder is 6
------------
((6^6)^6)^6… = 10*d+6 (d>=0) -->  reminder is 6

surya.427 · Answer

If we divide a number by 10, the remainder depends on the last digit of the number. For any last digit other than 0, the remainder is the same digit and for last digit as 0, the remainder when divided by 10 is 0. We can also say, 6^(any number) will give us the last digit of final result as 6. If we combine both of the above, dividing a number by 10 whose last digit is 6 will give us the remainder of 6.

RenKan90 · Answer

6.
No matter how many times you multiply 6 by itself, the number will always end in a 6. 
6*6=36
36*6 = 216
216 * 6 = xxx6

Why? Because the units digits will always be 6x6

The remainder when ((6^6)^6)^6… is divided by 10 is

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The remainder when ((6^6)^6)^6… is divided by 10 is

Prep Toolkit

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