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Number Theory

Number Theory Warmups

Last Digit Warmup

         

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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