What is the remainder when 3^7 is divided by 8?

Question

(A) 1
(B) 2
(C) 3
(D) 5
(E) 7

eswarchethu135 · Answer

\frac{3^7}{8}

=  \frac{(3^2)^3 *3}{8}

=  \frac{(9)^3 * 3}{8}

9 divided by 8 will always leave a remainder 1

=  \frac{(1)^3 * 3}{8}

=  \frac{3}{8}

Remainder = 3

OPTION:  C

EgmatQuantExpert · Answer

Solution

To find:  
 • Remainder when  3^7  is divided by 8

Approach and Working:  
 •  3^7  =  3^6  × 3 =  (3^2)^3  × 3 =  9^3  × 3

Remainder when  9^3  × 3 is divided by 8:
 •  (\frac{9^3 × 3}{8}) R =  (\frac{1^3 × 3}{8}) R = 3

Hence, the correct answer is option C.
 
  Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-NP-e1533292144892.png

Archit3110 · Answer

3^7 = 9*3^5
3^5 = cyclicity we get 3 
and 9 divided by 8 gives remainder 1 
1*3 = 3
IMO C

ScottTargetTestPrep · Answer

3^1/8 has a remainder of 3.

3^2/8 has a remainder of 1.

3^3/8 has a remainder of 3.

3^4/8 has a remainder of 1.

We see that when 3 raised to an odd power is divided by 8, the remainder is 3.

Answer: C

Shef08 · Answer

I did it in pure cyclist, 3^7 gives unit value of 7, and when 7/8 gives 7 as remainder? can any expert please tell me where I went wrong?

EgmatQuantExpert · Answer

Just units digit may not give you the remainder. For example, will you get the same remainder everytime when 7, 17, 27, 37 etc are divided by 8?

So, in case you are trying to determine the remainder by 7, just considering the units digit of the number is not the correct approach.

MHIKER · Answer

Why am I failing to apply the cyclicity formula 4? The cyclicity of 2,3,7 and 8 is 4
So I am dividing  \frac{7}{4}  and getting the remainder 3
 3^3   the unit digit is 7 
So  \frac{7}{8}  the remainder is 7 but, it is wrong. May I know why?  Bunuel

CrackverbalGMAT · Answer

CONCEPT: Remainders.

-Try to reach a 1 or a –1 by grouping the individual remainders.

SOLUTION: Group three 3s as one group giving you two 27s(3x3x3) and one 3 that remains
ungrouped.
Every 27 gives a (-1) on dividing by 7.
Thus, 3^7/ 7 -> 27x27x3/7 -> (-1) x (-1) x 3 /7
->3/7 = +3 as remainder. (c)
Hope this helps. Keep studying and growing.

All the Best!

Devmitra Sen

All the Best!

Devmitra Sen

BrushMyQuant · Answer

We need to find What is the remainder when  3^7  is divided by 8

Theory:  Remainder of a * b by a number say 8 is same as remainder of a by 8 * remainder of b by 8

3^7  =  3^{(2 + 2 + 2 + 1)}  =  3^2 * 3^2 * 3^2 * 3^1  = 3 *  3^2 * 3^2 * 3^2

=> Remainder of  3^7  by 8 is same as Remainder of 3 by 8 * Remainder of  3^2  by 8 * Remainder of  3^2  by 8 * Remainder of  3^2  by 8

= 3 * 1 * 1 * 1 = 3

So,  Answer will be C 
Hope it helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

https://www.youtube.com/watch?v=h1HTEhmUb1w

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What is the remainder when 3^7 is divided by 8?

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What is the remainder when 3^7 is divided by 8?

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