2. What is the remainder when $1234 \times 5678$ is divided by 5 ?
A 0
B 1
C 2
D 3
E 4
SOLUTION
C

The units digit of $1234 \times 5678$ is the same as the units digit of $4 \times 8$, and hence is 2 . Therefore the remainder when $1234 \times 5678$ is divided by 5 is 2 .

FOR INVESTIGATION
2.1 What is the remainder when $1234 \times 5678$ is divided by 3 ?
2.2 What is the remainder when $1234 \times 5678$ is divided by 11 ?
2.3 The integer $m$ has remainder 3 when it is divided by 11 . The integer $n$ has remainder 4 when divided by 11 .
What is the remainder when $m n$ is divided by 11 ?