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# 6^6 is equal to which of the following?

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Math Expert
Joined: 02 Sep 2009
Posts: 43361
6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 01:32
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98% (00:18) correct 2% (01:49) wrong based on 108 sessions

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6^6 is equal to which of the following?

A. 46,656
B. 48,752
C. 49,660
D. 50,662
E. 51,608
[Reveal] Spoiler: OA

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Re: 6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 01:46
A is the correct answer. We do not really need to calculate it. The last digit for 6^6 will be 6. Hence A is the correct answer
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Re: 6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 03:10
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rahuljha2511 wrote:
A is the correct answer. We do not really need to calculate it. The last digit for 6^6 will be 6. Hence A is the correct answer

Check

6^1 = 6
6^2 = 36
6^3 = 216

and so on............

One more thing to remember here is that 6 is a product of 2 and 3

So, we may say $$6^6$$ = $$(2*3)^6$$
So. whatever may be the result the number must be divisible by 2 and 3 both

Check the above property -

A. 46,656

1. Divisible by 2 as last digit (6 ) is even digit
2. Divisible by 3 as sum of all the digits ( 4+6+6+5+6 = 27 ) is divisible by 3

Hence I am double sure answer is (A)

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Joined: 09 Aug 2013
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Re: 6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 03:23
Bunuel wrote:
6^6 is equal to which of the following?

A. 46,656
B. 48,752
C. 49,660
D. 50,662
E. 51,608

Solution: ((63)2)=216*216=46656
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Re: 6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 04:01
in powers only 5 and 6 is multiplied so many times itself.
last digits will 5 and 6 respectively.

so option A only have 6 in last digit.

so option A is correct.
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Re: 6^6 is equal to which of the following? [#permalink]

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14 Apr 2016, 10:11
There is no need to calculate, 6^ of any power will be ending with units digit in 6.
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Re: 6^6 is equal to which of the following? [#permalink]

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15 Apr 2016, 01:27
The cyclicity of 6 is one => 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6...
Hence the UD will be 6
so A must be the choice
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Re: 6^6 is equal to which of the following? [#permalink]

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15 Apr 2016, 02:44
6^6 is equal to which of the following?

A. 46,656
B. 48,752
C. 49,660
D. 50,662
E. 51,608

2^6 * 3^3 * 3^3
64*27*27 = 7*7*4 = 6 (Units digit) It only matches with A.
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Re: 6^6 is equal to which of the following? [#permalink]

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05 Oct 2017, 05:12
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 6^6 is equal to which of the following?   [#permalink] 05 Oct 2017, 05:12
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