Number theory

$1\le 24n\le 10000\\ 1\le n\le 416$

Number of integers divisible by m less than n is given by the floor function as follows :

$\large \displaystyle \color{#3D99F6} \lfloor \frac{n}{m} \rfloor$

Answer is : $\large \displaystyle \color{#3D99F6} \lfloor \frac{1000}{24} \rfloor = \boxed{416}$

Simple. How many times does 24 go into 10,000?

10,000/24=416.6666=416

With A={4k: k ∈ N ∧ 4k ≤ 1000} all numbers that are devisible by 4 and with B={6k : k ∈ N ∧ 6k ≤ 10000} all nmbers that are devisible by 6 . And now we got A ∩ B = {12k : k ∈ N ∧ 12k ≤ 1000} or from multiple smaller common