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What is the smallest integer, which, when multiplied by 6 gives a number consisting of only 8's?

 [Ref: ZCXA] © Kevin Stone

148.

148 * 6 = 888.

The easiest way is to work backwards and divide successive 8's by 6 until you get an integer:

  8 ÷ 6 = 1.3333
 88 ÷ 6 = 14.666
888 ÷ 6 = 148.

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