Quiz — 6745c3c074a2d_Enoncé-arithmétique.pdf

Question 1 sur 5 10:00

[{"id":231,"question":"Quel est le PGCD de 120 et 180 ?","option_a":"20","option_b":"30","option_c":"60","option_d":"40","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le PGCD de 120 et 180 se calcule en décomposant chaque nombre en facteurs premiers : 120 = 2³ × 3 × 5 et 180 = 2² × 3² × 5. Le PGCD est le produit des facteurs premiers communs avec les plus petits exposants : 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\": \"c\", \"options\": {\"a\": \"20\", \"b\": \"30\", \"c\": \"60\", \"d\": \"40\"}}","_debug_options_count":4},{"id":232,"question":"Si a ≡ 3 (mod 7) et b ≡ 5 (mod 7), que vaut a + b (mod 7) ?","option_a":"1","option_b":"8","option_c":"0","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant les propriétés des congruences, a + b ≡ 3 + 5 ≡ 8 ≡ 1 (mod 7), car 8 - 1 = 7 est divisible par 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\", \"b\": \"8\", \"c\": \"0\", \"d\": \"5\"}}","_debug_options_count":4},{"id":233,"question":"Quelle est la décomposition en facteurs premiers de 84 ?","option_a":"2² × 3 × 7","option_b":"2 × 3² × 7","option_c":"2³ × 3 × 7","option_d":"2 × 3 × 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"84 se décompose en 2 × 42, puis 2 × 2 × 21, et enfin 2 × 2 × 3 × 7. Ainsi, 84 = 2² × 3 × 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2² × 3 × 7\", \"b\": \"2 × 3² × 7\", \"c\": \"2³ × 3 × 7\", \"d\": ","_debug_options_count":4},{"id":234,"question":"Quel est le PPCM de 15 et 20 ?","option_a":"30","option_b":"60","option_c":"120","option_d":"40","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PPCM se calcule en multipliant les facteurs premiers communs et non communs avec les plus grands exposants : 15 = 3 × 5 et 20 = 2² × 5. Le PPCM 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\": \"120\", \"d\": \"40\"}}","_debug_options_count":4},{"id":235,"question":"Si 7 divise ab et que 7 ne divise pas a, que peut-on conclure sur b selon le théorème de Gauss ?","option_a":"7 divise b","option_b":"b est un nombre premier","option_c":"b est impair","option_d":"b est pair","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Gauss stipule que si un nombre premier divise un produit ab et ne divise pas a, alors il doit diviser b. Ainsi, 7 divise 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\": \"7 divise b\", \"b\": \"b est un nombre premier\", \"c\": \"b est impair\",","_debug_options_count":4}]