Quiz — Série-29-Arithmétiques.pdf

Question 1 sur 10 20:00

[{"id":74180,"question":"Quel est le PGCD de 36 et 48 ?","option_a":"12","option_b":"6","option_c":"24","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 36 et 48 est 12, car c'est le plus grand nombre qui divise à la fois 36 et 48. On peut le vérifier en utilisant l'algorithme d'Euclide.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"12\", \"b\": \"6\", \"c\": \"24\", \"d\": \"8\"}}","_debug_options_count":4},{"id":74181,"question":"Deux entiers a et b sont premiers entre eux si leur PGCD est égal à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : deux entiers sont premiers entre eux si leur PGCD est 1, ce qui signifie qu'ils n'ont aucun diviseur commun autre que 1.","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":74182,"question":"Quel est le PPCM de 8 et 12 ?","option_a":"24","option_b":"48","option_c":"96","option_d":"16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PPCM (Plus Petit Commun Multiple) de 8 et 12 est 24, car c'est le plus petit nombre divisible à la fois par 8 et 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"24\", \"b\": \"48\", \"c\": \"96\", \"d\": \"16\"}}","_debug_options_count":4},{"id":74183,"question":"Si a ≡ b [n], alors n divise (a - b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : la notation a ≡ b [n] signifie que a et b ont le même reste dans la division par n, donc n divise (a - b).","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":74184,"question":"Quel est le résultat de 15 mod 4 ?","option_a":"3","option_b":"1","option_c":"7","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"15 divisé par 4 donne un quotient de 3 et un reste de 3, donc 15 mod 4 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"1\", \"c\": \"7\", \"d\": \"0\"}}","_debug_options_count":4},{"id":74185,"question":"Le théorème de Gauss stipule que si un nombre premier p divise un produit ab, alors p divise a ou p divise b.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : c'est l'un des théorèmes fondamentaux de l'arithmétique, utile pour démontrer des propriétés de divisibilité.","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":74186,"question":"Quel est le PGCD de 105 et 140 ?","option_a":"35","option_b":"70","option_c":"5","option_d":"210","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 105 et 140 est 35, car c'est le plus grand diviseur commun à ces deux nombres.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"35\", \"b\": \"70\", \"c\": \"5\", \"d\": \"210\"}}","_debug_options_count":4},{"id":74187,"question":"Si a et b sont deux entiers, alors PGCD(a, b) × PPCM(a, b) = a × b.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : cette relation est fondamentale en arithmétique et permet de relier PGCD et PPCM.","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":74188,"question":"Quel est le reste de la division de 2^10 par 7 ?","option_a":"2","option_b":"4","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"2^10 = 1024. 1024 divisé par 7 donne un reste de 2, car 7 × 146 = 1022 et 1024 - 1022 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"1\", \"d\": \"3\"}}","_debug_options_count":4},{"id":74189,"question":"Le théorème de Bézout s'applique uniquement si a et b sont premiers entre eux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : le théorème de Bézout stipule que si a et b sont premiers entre eux, alors il existe des entiers u et v tels que au + bv = 1.","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}]