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Warren Craig
08/28/2024 · High School

Exercice 2 : Un pâtissier a préparé 840 financiers et 1176 macarons. Il souhaite faire des lots de financiers et de macarons, tous identiques, en utilisant ses pâtisseries. 1) Le pâtissier peut - il faire 21 lots? Justifie. Si oui, donne la composition de chaque lot. 2) Trouve la décomposition en produits de facteurs premiers de 840. 3) Trouve la décomposition en produits de facteurs premiers de 1176. 4) Donne la liste des diviseurs de 840. 5) Donne la liste des diviseurs de 1176 . 6) Combien de lots peut - il faire au maximum? Justifie. 7) Quelle sera alors la composition de chaque lot? Justifie.

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1) Oui, le pâtissier peut faire 21 lots. Chaque lot contient 40 financiers et 56 macarons. 2) 840 = \(2^3 \times 3^1 \times 5^1 \times 7^1\). 3) 1176 = \(2^3 \times 3^1 \times 7^2\). 4) Diviseurs de 840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. 5) Diviseurs de 1176 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176. 6) Le pâtissier peut faire au maximum 24 lots. 7) Chaque lot contient 35 financiers et 49 macarons.

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