Question-106422

Question Number 106422 by Algoritm last updated on 05/Aug/20

Commented by mr W last updated on 05/Aug/20

73! = 1 \times 2 \times 3 \times \dots \times 49 \times 50 \times \dots \times 73

73! = 0 (m o d 2)

73! = 0 (m o d 3)

73! = 0 (m o d 4)

\dots

73! = 0 (m o d 49)

73! = 0 (m o d 50)

\dots

73! = 0 (m o d 73)

Answered by Olaf last updated on 24/Sep/20

73! = 48! \times 49 \times \frac{73!}{49!}

73! = 49 k with k = \frac{73!}{49}

\Rightarrow 73! \equiv 0 [49]

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