Quiz — Série d'exercices N°4 - Math Divisibilité dans N - 3ème Math (2014-2015) Mr Dhaouadi Ameur.pdf

Question 1 sur 10 20:00

[{"id":30300,"question":"Quel est le plus grand diviseur commun de 48 et 18 ?","option_a":"6","option_b":"12","option_c":"18","option_d":"24","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 48 et 18 est 6, car 48 = 2³ × 3 et 18 = 2 × 3², donc le PGCD est 2 × 3 = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6\", \"b\": \"12\", \"c\": \"18\", \"d\": \"24\"}}","_debug_options_count":4},{"id":30301,"question":"Un nombre est divisible par 9 si la somme de ses chiffres est divisible par 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un nombre est divisible par 9 si la somme de ses chiffres est divisible par 9, pas seulement par 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30302,"question":"Quel est le plus petit multiple commun de 12 et 15 ?","option_a":"30","option_b":"60","option_c":"90","option_d":"120","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PPCM de 12 (2² × 3) et 15 (3 × 5) est 2² × 3 × 5 = 60.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"30\", \"b\": \"60\", \"c\": \"90\", \"d\": \"120\"}}","_debug_options_count":4},{"id":30303,"question":"Si a divise b et b divise c, alors a divise c.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la divisibilité : la relation de divisibilité est transitive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30304,"question":"Quel est le reste de la division de 1234 par 7 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"d","explication":"1234 ÷ 7 = 176 reste 2, car 7 × 176 = 1232 et 1234 - 1232 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":30305,"question":"Le nombre 1 est un nombre premier.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, un nombre premier a exactement deux diviseurs distincts : 1 et lui-même. Le nombre 1 n'a qu'un seul diviseur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30306,"question":"Quel est le PGCD de 210 et 462 ?","option_a":"6","option_b":"14","option_c":"21","option_d":"42","option_e":"","option_f":"","bonne_reponse":"d","explication":"210 = 2 × 3 × 5 × 7 et 462 = 2 × 3 × 7 × 11, donc PGCD = 2 × 3 × 7 = 42.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"6\", \"b\": \"14\", \"c\": \"21\", \"d\": \"42\"}}","_debug_options_count":4},{"id":30307,"question":"Si un nombre est divisible par 4 et par 6, alors il est divisible par 24.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un nombre divisible par 4 et 6 est divisible par leur PPCM, qui est 12, mais pas nécessairement par 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30308,"question":"Quel est le plus petit nombre premier supérieur à 50 ?","option_a":"51","option_b":"53","option_c":"55","option_d":"57","option_e":"","option_f":"","bonne_reponse":"b","explication":"53 est le plus petit nombre premier supérieur à 50 (51 = 3 × 17, 55 = 5 × 11, 57 = 3 × 19).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"51\", \"b\": \"53\", \"c\": \"55\", \"d\": \"57\"}}","_debug_options_count":4},{"id":30309,"question":"Le théorème de Gauss s'applique uniquement aux nombres premiers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Gauss s'applique à tout couple d'entiers premiers entre eux, pas uniquement aux nombres premiers.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]