math intel

768 = 2 x 384
= 2² x 192
= 2³ x 96
= 2^4 x 48
= 2^5 x 24
= 2^6 x 12
= 2^7 x 6
= 2^8 x 3

1000 = 10³
= 2³ x 5³

All multiples of 1000 are divisible by 2³ and 768 is divisible by 2³. The greatest common factor of 1000 and 768 is 2³.

So the answer is 8.