This document discusses divisibility rules that can help determine if a number is divisible by other numbers without calculating remainders. It provides the rules for divisibility by 2, 5, 10, 3, 9, and 6. The rules state that a number is divisible by 2 if it is even, by 5 if it ends in 0 or 5, by 10 if it ends in 0, by 3 if the sum of its digits is divisible by 3, by 9 if the sum of its digits is divisible by 9, and by 6 if it is divisible by both 2 and 3. An example is worked out for each rule.