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Guest Message by DevFuse

One's divisibility

Started by Prime, Feb 09 2013 08:34 PM

Best Answer googon97, 09 February 2013 - 09:36 PM

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2 replies to this topic

#1 Prime

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Posted 09 February 2013 - 08:34 PM

Find the smallest number consisting of only "1"-s,

which would be divisible by "333...3" (one hundred "3"-s.)

(Decimal system.)

0

Past prime, actually.

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#2 googon97

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Posted 09 February 2013 - 09:36 PM Best Answer

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#3 Prime

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Posted 10 February 2013 - 12:44 AM

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3333....3 is 3*1111....1
The number consisting of only ones must be a multiple of 3 and 1111...1. For it to be a multiple of 111....1, it must be a multiple of 100 1's long. The first multiple of 100 divisible by 3 is 300. So, the number is 111...1 with 300 1's.

That's the number I was looking for!

Edited by Prime, 10 February 2013 - 12:44 AM.

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Past prime, actually.

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