有一个四位数8AAB，它有因数2和3，同时又是5的倍数，这个四位数可能是多少？ 有一个四位数8aab，它有因数2和3，同时又是5的倍数，这个...
\u6709\u4e00\u4e2a\u56db\u4f4d\u65708AAB\uff0c\u5b83\u6709\u56e0\u65702\u548c3\uff0c\u540c\u65f6\u53c8\u662f5\u7684\u500d\u6570\uff0c\u8fd9\u4e2a\u56db\u4f4d\u6570\u53ef\u80fd\u662f\u591a\u5c11\uff1f\u89e3\u7b54\uff1a\u4e00\u4e2a\u6570\u65e2\u662f2\u7684\u500d\u6570\u53c8\u662f5\u7684\u500d\u6570\uff0c\u5b83\u7684\u4e2a\u4f4d\u6570\u5b57\u4e00\u5b9a\u65f60\uff0c\u800c\u4e00\u4e2a\u6570\u80fd\u88ab3\u6574\u9664\uff0c\u5b83\u7684\u5404\u4e2a\u6570\u4f4d\u4e0a\u7684\u6570\u5b57\u4e4b\u548c\u4e00\u5b9a\u65f63\u7684\u500d\u6570\uff0c\u56e0\u6b64\uff0cB\u662f0\uff0cA\u662f2\u62165\u62168.\u8fd9\u4e2a\u56db\u4f4d\u6570\u53ef\u80fd\u662f\uff1a8820\u30018550\u30018880.
\u89e3\u7b54\uff1a\u4e00\u4e2a\u6570\u65e2\u662f2\u7684\u500d\u6570\u53c8\u662f5\u7684\u500d\u6570\uff0c\u5b83\u7684\u4e2a\u4f4d\u6570\u5b57\u4e00\u5b9a\u65f60\uff0c\u800c\u4e00\u4e2a\u6570\u80fd\u88ab3\u6574\u9664\uff0c\u5b83\u7684\u5404\u4e2a\u6570\u4f4d\u4e0a\u7684\u6570\u5b57\u4e4b\u548c\u4e00\u5b9a\u65f63\u7684\u500d\u6570\uff0c\u56e0\u6b64\uff0cB\u662f0\uff0cA\u662f2\u62165\u62168.\u8fd9\u4e2a\u56db\u4f4d\u6570\u53ef\u80fd\u662f\uff1a8820\u30018550\u30018880.
2*3*5=30B=0
A=2,5,8
这个四位数可能是8220,8550,8880
8220
8550
因为A应该不能是8，排除掉8880
绛旓細瑙ｇ瓟锛涓涓鏁版棦鏄2鐨勫嶆暟鍙堟槸5鐨勫嶆暟锛屽畠鐨勪釜浣嶆暟瀛椾竴瀹氭椂0锛岃屼竴涓暟鑳借3鏁撮櫎锛屽畠鐨勫悇涓暟浣嶄笂鐨勬暟瀛椾箣鍜屼竴瀹氭椂3鐨勫嶆暟锛屽洜姝わ紝B鏄0锛孉鏄2鎴5鎴8.杩欎釜鍥涗綅鏁鍙兘鏄細8820銆8550銆8880.
绛旓細5鐨勫嶆暟锛屾渶鍚庝竴浣嶆暟鏄0鎴5锛屽張鍥犱负鏈鍥犳暟2鎵浠ユ湯浣嶄负0锛屽洜涓烘湁鍥犳暟3锛屾墍浠8锛2A锛0鏄笁鐨勫嶆暟锛孉涓哄皬浜10鐨勬鏁存暟鎵浠=2锛5锛8鎵浠ヨ繖涓暟鏄8220鎴8550鎴2880
绛旓細B=0 A=2,5,8 杩欎釜鍥涗綅鏁鍙兘鏄8220,8550,8880
绛旓細2脳3脳5=30锛屾墍浠鏄0,8+A+A涓瀹氭槸3鐨勫嶆暟锛孉鍙兘鏄2,5,8.
绛旓細鍏堝畾B锛氬洜涓烘槸5鍙堟槸2鐨勫嶆暟锛屾墍浠鍙兘鏄0銆傚啀瀹欰锛8A10锛屽悇浣嶆暟鐨勫拰鏄8+A+1+0=9+A搴斿綋鏄3鐨勫嶆暟锛屽垯 A=0, 3, 6, 9閮藉彲浠ャ傛墍浠ヨ繖涓鍥涗綅鏁版湁4绉嶅彲鑳斤細8010, 8310, 8610, 8910.
绛旓細鏈変竴涓洓浣嶆暟瀹冪殑鍗冧綅鏄鍏紝瀹冩湁鍥犳暟浜屽拰涓夛紝鍚屾椂鍙堟槸浜旂殑鍊嶆暟杩欎釜鍥涗綅鏁板彲鑳芥槸锛8010锛8040,8070锛8100,8130,8160,8190,8220,8250,8280,8310,8340,8370锛8400,8430,8460,8490,8520,8550,8580,8610,8640,8670锛8700,8730,8760,8790,8820,8850,8880,8910,8940,8970....
绛旓細鍥犳暟2鎵浠ユ柟妗嗛噷鏄伓鏁,鍥犳暟3鐨勮瘽3+5+8+妗=16+妗,鏄3鐨勫嶆暟,鎵浠ユ鏈灏=2,涔熷氨鏄3582.璇烽噰绾炽
绛旓細褰撲釜浣涓婃槸0鐨勬椂鍊欙紝鑳借5鏁撮櫎锛岀粍鏁版槸锛6280锛屽洜涓6+2+8+0=16锛屾墍寰楃殑鍜16涓嶆槸3鐨勫嶆暟锛屼笉鑳借3鏁撮櫎锛屾墍浠ヤ釜浣嶄笂涓嶆槸0锛庡綋涓綅涓婃槸5鐨勬椂鍊欙紝鑳借5鏁撮櫎锛岀粍鎴愮殑鏁版槸锛6285锛6+2+8+5=21锛屾槸3鐨勫嶆暟锛屾墍浠ヨ繖涓暟涓綅涓婃槸5锛涙晠绛旀涓猴細5锛
绛旓細搴旇鏄細5 鏈夊洜鏁5锛岃鏄庡彛閲屽簲濉暟瀛0鎴5 鍙堝洜涓烘湁鍥犳暟3锛岄偅涔堣鍥涗綅鏁鎵鏈夋暟瀛椾箣鍜屽簲璇ヨ兘澶熻3鏁撮櫎 鍋囧涓綅鏄0锛岄偅涔堟湁6+2+8+0=16,16梅3=5...1锛鎵浠ュ彛閲屼笉鑳藉～0.鍋囧涓綅鏄5锛岄偅涔堟湁6+2+8+5=21,21梅3=7锛屾墍浠ュ彛閲岃兘濉5.鎵浠ュ簲璇ユ槸5 璋㈣阿锛岃閲囩撼 ...
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