Burns Chavez
05/12/2024 · Middle School
Exercice (1) On considère les nombres \( \boldsymbol{a}=\mathbf{2 4 0 0} \) et \( \boldsymbol{b}=\mathbf{1 3 5 0} \) 1) Décomposer \( \boldsymbol{a} \) et \( \boldsymbol{b} \) en produit de facteurs premiers. 2) Déduire \( \boldsymbol{p g c d}(\boldsymbol{a}, \boldsymbol{b}) \) et \( \boldsymbol{p p c m}(\boldsymbol{a}, \boldsymbol{b}) \) 3) Simplifier le nombre \( \frac{\boldsymbol{a}}{\boldsymbol{b}} \). 4) Montrer que \( \sqrt{a b} \) est un entier naturel. 5) Déterminer le plus petit naturel \( \boldsymbol{m} \) non nul pour que le nombre \( \boldsymbol{m b} \) soit un cube d'un entier naturel. 6) Le nombre 127 est-il premier ? justifier la réponse.
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1) \( a = 2^4 \times 3 \times 5^2 \), \( b = 2 \times 3^3 \times 5 \)
2) PGCD(a, b) = 30, PPCM(a, b) = 10800
3) \( \frac{a}{b} = \frac{8}{9} \)
4) \( \sqrt{a b} = 1800 \) est un entier naturel
5) \( m = 24 \) pour que \( m b \) soit un cube d'un entier naturel
6) 127 est premier
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