Number Theory

Number Theory Warmups

Last Digit Warmup

         

What is the last digit of

123×321? 123 \times 321 ?

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

What is the last digit of

123+321? 123 + 321 ?

What is the last digit of

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

What is the last digit of

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

What is the last digit of

1234×5678? 1234 \times 5678 ?

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