What is the remainder when 3^50 is divided by 4?

Question

What is the remainder when  3^5^0  is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

koenh · Accepted Answer

Rewrite  3^{50}  as  (3^{2})^{25} = 9^{25} .

9^{25} = (8+1)^{25} . Now  8^{25}  will always be divisible by 4 and leaves remainder 0.  1^{25}  = 1 and leaves remainder 1.

Answer B.

Abhishek009 · Answer

3^{50} = 9^{25}

\frac{9}{4}  = Remainder 1

So,  9^{25}  , will have remainer as 1
  
Answer will be (B) 1

MathRevolution · Answer

==> The units digit of  3^n  is the repetition of  3-->9-->7--->1-->3-->9-->7-->1 , so you get  50=4*12+2 . 
Thus, from  3^5^0=3^4^*^1^2^+^2  -->  ~3^2=~9 , the units digit becomes 9, and if you divide it by 4, from  9=4*2+1 , the remainder becomes 1. 
Therefore, the answer is B.
Answer: B

Loser94 · Answer

hat is the remainder when 3^50 is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

unit digit of powers of 3 follows a pattern of 4 (3,9,7,1) 
So we divide 50/4=2 remainder which means power of 2 will be there 
3 power 2= 9
9/4=1 remainder adn our answer

Option B (1)

ScottTargetTestPrep · Answer

Since 3 = 4 - 1, we can think 3 as “-1” when it’s divided by 4. Therefore, the remainder when 3^50 is divided by 4 is same as the remainder when (-1)^50 is divided by 4. So the remainder is (-1)^50 = 1.

Answer: B

TheNightKing · Answer

You should use negative remainders. (If you're comfortable)

3/4 gives remainder of -1.

(-1)^50  is 1 since it is raised to an even power.

Hence B

Aditi31 · Answer

Is it possible to apply the divisibility rule only on the unit's place?

bumpbot · Answer

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What is the remainder when 3^50 is divided by 4?

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What is the remainder when 3^50 is divided by 4?

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