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Unit's digit of large factorials with exponents?

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Unit's digit of large factorials with exponents? [#permalink]

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New post 23 Nov 2017, 01:04
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if

\(\frac{((13!)^{16} -(13!)^8)}{(13!)^8+(13!)^4}\) = a




then what is the unit's digit of \(\frac{a}{(13!)^4}\)


A) 0
B) 1
C) 3
D) 5
E) 9


Any input is appreciated, since I don't even know where to start on this one.
[Reveal] Spoiler: OA

Kudos [?]: 0 [0], given: 0

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Joined: 02 Sep 2009
Posts: 42630

Kudos [?]: 135803 [0], given: 12714

Re: Unit's digit of large factorials with exponents? [#permalink]

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New post 23 Nov 2017, 01:08
sebcroy wrote:
if

\(\frac{((13!)^{16} -(13!)^8)}{(13!)^8+(13!)^4}\) = a




then what is the unit's digit of \(\frac{a}{(13!)^4}\)


A) 0
B) 1
C) 3
D) 5
E) 9


Any input is appreciated, since I don't even know where to start on this one.


Discussed here: https://gmatclub.com/forum/if-a-13-1-6- ... 65186.html Hope it helps.
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Kudos [?]: 135803 [0], given: 12714

Re: Unit's digit of large factorials with exponents?   [#permalink] 23 Nov 2017, 01:08
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