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Finding Last Digits

Finding Last Digits

Lesson · Beginner

Number Theory

Find the last 3 digits of 23578 × 16327

Finding the last three digits of 23578 times 16327

Modular Arithmetic

Find the last 3 digits of 38 × 39 × 41 × 42

38\cdot39\cdot41\cdot42 \pmod{1000}

=(40-2)(40-1)(40+1)(40+2)

=(40-2)(40+2)(40-1)(40+1)

=(40^2-2^2)(40^2-1^2)

=(1600-4)(1600-1)

=1600^2-5\cdot1600+4 \pmod{1000}

\equiv0-8000+4\equiv4\pmod{1000}

\boxed{004}

Find the last 4 digits of

246783\times987435

Finding the last four digits of 246783 times 987435

\boxed{1605}

AMC 12B 2025 (Problem 9)

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