Question

How many positive integers less than 2101 are divisible by at least one of the primes 2,3,5, or 7

Answer 1

which course are you taking? im not sure whether to give this a trial-and-error approach or not

Answer 2

I don't know whether there is a faster way of doing this.

Clearly, all the evens are div 2.

And 3, 5, 7 are div ,3,5,7.

For the rest of the odds, they will all be div by one of 3,5,7 (or 9, which implies 3) except the primes.

So it seems the question involves counting the primes between 10 and 2100 and subtracting that from 2100 for your answer.

Since I don't know of any formula for that, you might as well just get a list of primes from somewhere and count them (or use a programmatic sieve).