Which of the following is a divisibility rule for 9?

• A. The sum of digits is divisible by 9
• B. The last digit is 9
• C. The product of digits is divisible by 9
• D. The number ends with 0

Answer: (A)

Divisibility by 9 is tested by the sum-of-digits rule. Because 10 ≡ 1 (mod 9), a number written in base 10 is congruent to the sum of its digits modulo 9. So the number is divisible by 9 exactly when that digit sum is divisible by 9.

For example, a number like 981 has digits 9, 8, and 1; their sum is 18, which is divisible by 9, so 981 is divisible by 9 (indeed 109 × 9 = 981).

Other statements don’t hold as universal tests: ending with 9 isn’t enough to ensure divisibility by 9 (e.g., 19 isn’t divisible by 9), the product of digits isn’t a reliable indicator, and ending with 0 tests divisibility by 10, not by 9.