Here's (b)....it's pretty much an extension of (a)

1000/7 = 142 numbers that have at least 1 factor of 7

1000/49 = 20 numbers that have at an additional factor of 7

1000/343 = 2 numbers that have a third factor of 7

So......... 142 + 20 + 1 = 163

And 7^163 will divide 1000! ...so n = 163