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.
8.
0.6667
23 is an odd number between 10 and 30 that gives a remainder of 2 when divided by 7.
89
69.
8
12 is the smallest whole number that gives a remainder of 4 when it is divided by 8.
8.
0.6667
3
23, 58, 93, 128, 163, 198, ...
40
23 is an odd number between 10 and 30 that gives a remainder of 2 when divided by 7.
3 divided by 2 goes once, remainder one.
172
89
69.