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Find the units digit of 333^333

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Find the units digit of 333^333  [#permalink]

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New post 29 Jan 2019, 05:18
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:35) correct 31% (01:03) wrong based on 45 sessions

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Re: Find the units digit of 333^333  [#permalink]

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New post 29 Jan 2019, 05:26
Bunuel wrote:
Find the units digit of 333^333

A. 1
B. 3
C. 5
D. 7
E. 9


units digit of 333^333 ==> 3^333

cyclicity of 3 is 4 hence 3^(332+1) ==> 3^1

Hence B(3)
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Re: Find the units digit of 333^333  [#permalink]

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New post 29 Jan 2019, 05:26
Bunuel wrote:
Find the units digit of 333^333

A. 1
B. 3
C. 5
D. 7
E. 9


333^333
=> 3^333 * 111^333

cyclicality of 3^333 would give us units as 3
and 1^333; 1
so 3*1 = 3
IMO B
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Find the units digit of 333^333  [#permalink]

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New post 29 Jan 2019, 10:38
check for power 333
3 has a cyclic repetition of 4. so unit digit of \(3^1\) is same as\(3^5\)
so lets divide 333 by 4.
this leaves a remainder of 1. Hence \((333)^(333)\) will be same as \(3^1\) = 3.
Thus B is the answer
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Re: Find the units digit of 333^333  [#permalink]

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New post 29 Jan 2019, 10:50
Bunuel wrote:
Find the units digit of 333^333

A. 1
B. 3
C. 5
D. 7
E. 9


For \(3^n\), unit digit will have a cyclicity pattern as 3 9 7 1

4|333|83, remainder is 1, signifies 1st position

Answer B
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Re: Find the units digit of 333^333  [#permalink]

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New post 31 Jan 2019, 17:48
Bunuel wrote:
Find the units digit of 333^333

A. 1
B. 3
C. 5
D. 7
E. 9


Since we care only about units digits, we can rewrite the expression as:

3^333

We can evaluate the pattern of the units digits of 3^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 3. When writing out the pattern, notice that we are ONLY concerned with the units digit of 3 raised to each power.

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

The pattern of the units digit of powers of 3 repeats every 4 exponents. The pattern is 3–9–7–1. In this pattern, all positive exponents that are multiples of 4 will produce a 1 as its units digit. Thus:

3^332 has a units digit of 1, so 3^333 has a units digit of 3.

Answer: B
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Re: Find the units digit of 333^333   [#permalink] 31 Jan 2019, 17:48
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