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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?  [#permalink]

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New post 06 Dec 2016, 01:56
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What is the remainder when \(3^5^0\) is divided by 4?

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

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What is the remainder when 3^50 is divided by 4?  [#permalink]

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New post Updated on: 06 Dec 2016, 08:45
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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.

Originally posted by koenh on 06 Dec 2016, 02:26.
Last edited by koenh on 06 Dec 2016, 08:45, edited 2 times in total.
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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New post 06 Dec 2016, 08:11
MathRevolution wrote:
What is the remainder when \(3^5^0\) is divided by 4?

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

\(3^{50} = 9^{25}\)

\(\frac{9}{4}\) = Remainder 1

So, \(9^{25}\) , will have remainer as 1

Answer will be (B) 1

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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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New post 08 Dec 2016, 01:44
==> 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
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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New post 22 Aug 2018, 12:59
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)
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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New post 26 Aug 2018, 18:22
MathRevolution wrote:
What is the remainder when \(3^5^0\) is divided by 4?

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


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
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Re: What is the remainder when 3^50 is divided by 4?   [#permalink] 26 Aug 2018, 18:22
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