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There is no such number since once you have found one, subtracting a multiple of 6 will give a lower number which will meet the requirement. So, for example, -599, or -5999 or -5999999999 all leave a remainder of 1 , but you can go still lower.

The lowest positive integer is, of course, 1.

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Q: What is the lowest number divided by 6 gives remainder 1?
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