Number Theory
# Number Theory Warmups

What is the last digit of

$123 \times 321 ?$

**Hint:** There is no need to completely multiply these numbers.

What is the last digit of

$123 + 321 ?$

What is the last digit of

$1 \times 3 \times 5 \times 7 \times 9 ?$

What is the last digit of

$1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 ?$

What is the last digit of

$1234 \times 5678 ?$