No-divisibility condition

What this divisibility-counting puzzle tests

This is an easy combinatorial counting problem that appears frequently in quant interviews as a quick warm-up or screening question. It tests whether you can apply the inclusion–exclusion principle to count integers satisfying a no-divisibility condition over a finite range.

The core skill is setting up the constraint systematically: identify which multiples to exclude, account for overlaps (integers divisible by more than one forbidden divisor), and subtract them from the total. Many candidates arrive at the answer fastest by structuring the problem as a series of set complements, rather than trying to enumerate directly.

• Inclusion–exclusion principle
• Counting multiples in a range
• Overlapping constraints and greatest common divisors