## Task 1 - 170931

Determine the number of natural numbers from 1 to 1000 (including these limits) that are not divisible by 2, 3, or 5!
It is $2 \cdot 3 \cdot 5=30$, so the pattern of remainders when dividing by 2, 3, and 5 repeats every 30 numbers. Of every 30 consecutive natural numbers, exactly 15 are odd. Of these 15 consecutive odd numbers, exactly five are divisible by 3, exactly three are divisible by 5, and exactly one is divisible by 15, so exactly $15-5-3+1=8$ numbers in such a 30-number block are not divisible by 2, 3, or 5.

Thus, in the 33 30-number blocks from 1 to $33 \cdot 30=990$, there are exactly $33 \cdot 8=264$ numbers that are not divisible by 2, 3, or 5. Additionally, 991 and 997 are included, as the remaining odd numbers from 991 to 1000 are divisible by 3 (993, 999) or by 5 (995).

Therefore, there are a total of 266 such numbers in the considered interval.