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# For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value o

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For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value o  [#permalink]

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25 Jul 2017, 11:19
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Question Stats:

50% (00:47) correct 50% (01:13) wrong based on 6 sessions

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For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value of the first non-zero digit from the right?

A) 1
B) 2
C) 4
D) 6
E) 8

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Re: For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value o  [#permalink]

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25 Jul 2017, 11:37
2
Take out the 10s (the 2*5 pairs) and we have:

n = 2^5 * 5^5 * 2^11 * 3^13 * 7^5 * 11^3
n = 10^5 * ( 2^11 * 3^13 * 7^5 * 11^3 )

All the zeros at the end of the number come from the 10^5. The first nonzero digit (from the right) will be the units digit of the number in brackets. So this is now a units digits problem. The units digit of 11^3 is '1', the units digit of 7^5 is 7, the units digit of 3^13 is '3', and the units digit of 2^11 is '8' (anyone unsure how I found those should review units digits and exponents). Multiplying just these units digits, we get

1*7*3*8

which ends in 8.

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Re: For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value o   [#permalink] 25 Jul 2017, 11:37
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