Divisibility

• How to Count Elements Divisible by Exactly Two of Three Numbers
  To count elements divisible by exactly two of three divisors, add the three pairwise counts and subtract three times the count divisible by all three.
• How to Count Integers Not Divisible by 5
  To count integers not divisible by 5, subtract the multiples of 5 from the total; use floor formulas for any interval or digit rule.
• What Is the Divisibility-by-7 Rule, and Why Does It Work?
  Test divisibility by 7 by subtracting twice the last digit from the remaining number; congruence arithmetic explains why the rule works.