6. How many positive integers not exceeding 1000 are divisible by 3 or 5 or 7?

1000/3=333

1000/5=200

1000/7=142

so, 333+200+142=675

There are 333 positive integers divisible by 3 less than 1000.

(1000/3) = 333

There are 199 positive integers divisible by 5 less than 1000.

(1000/5) = 199

There are 142 positive integers divisible by 7 less than 1000.

[1000/7] = 142