Determine the smallest number constituted entirely by sevens and zeroes which is divisible by 61376.

How about for 107072?

(In reply to

And the second part. (Spoiler) by Leming)

Okay, please help me out on this one. I figured out that factoring the divisor would be important, and each of the problems had factors of several 2s, one 7, and one larger prime. So if you can take the factor of seven out of the problem and just look for the smallest number consisting of 1s and 0s.

My question is how does that translate into finding all 1s with that large prime as a factor?