What is the remainder when $1{,}234 \times 5{,}678$ is divided by 9?

Explanation

1. 01

   1,234 has digit sum 10, so it leaves remainder 1 on division by 9.

2. 02

   5,678 has digit sum 26, so it leaves remainder 8.

3. 03

   Product of remainders = $1 \times 8 = 8$, so the remainder is 8.