# Thread: divisibility problem

1. ## divisibility problem

How many different positive integers less than 1000 are divisible by 7 but not 11?

how do i do this without explicitly checking each multiple of 7 or 11 less than 1000?

2. Originally Posted by jmedsy
How many different positive integers less than 1000 are divisible by 7 but not 11?

how do i do this without explicitly checking each multiple of 7 or 11 less than 1000?
Use the floor function: $\left\lfloor {\frac{{1000}}{7}} \right\rfloor - \left\lfloor {\frac{{1000}}{{77}}} \right\rfloor$.

3. Originally Posted by Plato
Use the floor function: $\left\lfloor {\frac{{1000}}{7}} \right\rfloor - \left\lfloor {\frac{{1000}}{{77}}} \right\rfloor$.
thanks, i just came up with that