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# Number Theory Warmups

If numbers aren't beautiful, we don't know what is. Dive into this fun collection to play with numbers like never before, and start unlocking the connections that are the foundation of Number Theory.

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

\[ 1234 \times 5678 ? \]

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