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Find the smallest positive base-10 integer composed entirely of 1's and 0's that is divisible by \(225\).

 Feb 6, 2022
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225  x  1==225

225 x   2==450

225  x  3 ==675

225 x   4==900 [ All these are multiples of 225.] However, multiples of 900 which must all be "1s" and "0s" implies that we must have at least 9 "ones" + the two "0s" of 900. So, the multiple of 900 must necessarily be: 11,111,111,100 which is mod 900==0, and consequently mod 225 ==0.

 Feb 6, 2022

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