Divisibility rules are methods used to determine whether a number can be evenly divided by another without performing full division. These rules simplify calculations and help identify factors quickly. For example, a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, and by 5 if it ends in 0 or 5. Familiarity with these rules enhances mental math and understanding of number properties.