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What is the units digit of the above expression?

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What is the units digit of the above expression? [#permalink]

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New post 18 Nov 2012, 04:02
(2^18)*(3^17)*(7^14)*(5^20)

What is the units digit of the above expression?

A. 0
B. 2
C. 5
D. 7
E. 9

Last edited by Bunuel on 18 Nov 2012, 04:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the units digit of the above expression? [#permalink]

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New post 18 Nov 2012, 07:42
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stef91 wrote:
(2^18)*(3^17)*(7^14)*(5^20)

What is the units digit of the above expression?

A. 0
B. 2
C. 5
D. 7
E. 9


Please note:
cyclicity of 2 is 4
cyclicity of 3 is 4
cyclicity of 7 is 4
cyclicity of 5 is 1.
So divide the respective powers by the integer's own cyclicity.
So the above expression can be written as:
\(2^2 * 3^3 * 7^2 * 5\)
It becomes \(4*27*49*5\)
Since 4*5=20,
so any number, if multiplied by 0 will yield 0 as the last digit.

Hence A.
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Re: What is the units digit of the above expression?   [#permalink] 18 Nov 2012, 07:42
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What is the units digit of the above expression?

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