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6. Le nombre démultiplié

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6. Le nombre démultiplié

Soit un nombre de 2 chiffres (ab). Pourquoi tout nombre de 2 chiffres multiplié successivement par 3, 7, 13 et 37 donne ababab ?

Autrement dit, pourquoi ab.3.7.13.37 = ababab ? Exemple : 85.3.7.13.37 = 858'585.

Solution

3.7.13.37 = 10'101. Notre multiplication revient à faire ab.10'101 = ab.(10'000 + 100 + 1)

= 10'000 . ab + 100 . ab + ab = ab0000 + ab00 + ab = ababab. Si vous n’avez pas compris, effectuez en détail le produit de 10'101 par 85 (exemple où ab = 85) et vous verrez pourquoi vous obtenez 858'585.

Augustin Genoud, avril 2013

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