{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[["3"]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/4.jpg' \/><\/center> <br\/> H\u00e3y ch\u1ecdn ph\u00e9p t\u00ednh n\u00e0o c\u00f3 k\u1ebft qu\u1ea3 l\u00e0 s\u1ed1 kh\u00f4ng chia h\u1ebft cho 3","select":["A. $729^{927} + 927^{729}$","B. $381^{2002} + 18^{2002}$","C. $49^{115} + 3^{2016}$","D. $81^{421} + 9342$"],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t chia h\u1ebft c\u1ee7a m\u1ed9t t\u1ed5ng ta x\u00e9t t\u1eebng s\u1ed1 h\u1ea1ng","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> N\u1ebfu trong t\u1ed5ng c\u00f3 m\u1ed9t s\u1ed1 h\u1ea1ng kh\u00f4ng chia h\u1ebft cho m\u1ed9t s\u1ed1 c\u00f2n c\u00e1c s\u1ed1 h\u1ea1ng c\u00f2n l\u1ea1i \u0111\u1ec1u chia h\u1ebft cho s\u1ed1 \u0111\u00f3 th\u00ec t\u1ed5ng chia h\u1ebft cho s\u1ed1 \u0111\u00f3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> A - S\u1ed1 729 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 2 + 9 = 18 <br\/> V\u00ec 18 $\\vdots$ 3 $\\Rightarrow$ 729 $\\vdots$ 3 $\\Rightarrow$ $729^{927}$ $\\vdots$ 3 <br\/> S\u1ed1 927 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 2 + 7 = 18 <br\/> V\u00ec 18 $\\vdots$ 3 $\\Rightarrow$ 927 $\\vdots$ 3 $\\Rightarrow$ $927^{729}$ $\\vdots$ 3 <br\/> $\\Rightarrow$ $(729^{927} + 927^{729})$ $ \\vdots$ 3 <br\/> B - S\u1ed1 381 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 3 + 8 + 1 = 12 <br\/> V\u00ec 12 $\\vdots$ 3 $\\Rightarrow$ 381 $\\vdots$ 3 $\\Rightarrow$ $381^{2002}$ $\\vdots$ 3 <br\/> $18^{2002}$ $\\vdots$ 3 (v\u00ec 18 $\\vdots$ 3) <br\/> $\\Rightarrow$ $(381^{2002} + 18^{2002})$ $\\vdots$ 3 <br\/> C - $49^{115}$ $\\not \\vdots$ 3 (v\u00ec 49 $\\not \\vdots$ 3) v\u00e0 $3^{2016}$ $\\vdots$ 3 <br\/> $\\Rightarrow$ ($49^{115} + 3^{2016}$) $\\not \\vdots$ 3 <br\/> D - $81^{421}$ $\\vdots$ 3 (v\u00ec 81 $\\vdots$ 3) <br\/> S\u1ed1 9342 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 3 + 4 + 2 = 18 <br\/> V\u00ec 18 $\\vdots$ 3 $\\Rightarrow$ 9342 $\\vdots$ 3 <br\/> $\\Rightarrow$ $(81^{421} + 9342)$ $\\vdots$ 3 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> ","column":2}]}],"id_ques":551},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[["3"]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/3.jpg' \/><\/center> <br\/> H\u00e3y ch\u1ecdn s\u1ed1 chia 5 d\u01b0 3 v\u00e0 chia 9 d\u01b0 3","select":["A. 38493","B. 87463","C. 92388","D. 93148"],"hint":"X\u00e9t ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng v\u00e0 t\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ch\u1ecdn s\u1ed1 chia 5 d\u01b0 3 b\u1eb1ng c\u00e1ch x\u00e9t ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a c\u00e1c s\u1ed1 v\u1eeba ch\u1ecdn \u1edf b\u01b0\u1edbc 1 \u0111\u1ec3 t\u00ecm s\u1ed1 chia 9 d\u01b0 3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> V\u00ec nh\u1eefng s\u1ed1 c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 0, 5 th\u00ec chia h\u1ebft cho 5 <br\/> N\u00ean s\u1ed1 chia 5 d\u01b0 3 c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 0 + 3 = 3 ho\u1eb7c 5 + 3 = 8 <br\/> V\u1eady t\u1ea5t c\u1ea3 c\u00e1c \u0111\u00e1p \u00e1n tr\u00ean khi chia 5 \u0111\u1ec1u d\u01b0 3, t\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 <br\/> S\u1ed1 38493 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 3 + 8 + 4 + 9 + 3 = 27 <br\/> V\u00ec 27 $\\vdots$ 9 $\\Rightarrow$ 38493 $\\vdots$ 3 <b> (lo\u1ea1i) <\/b> <br\/> S\u1ed1 87463 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 8 + 7 + 4 + 6 + 3 = 28 <br\/> V\u00ec 28 = 3.9 + 1 n\u00ean 28 chia 9 d\u01b0 1 hay 87463 chia 9 d\u01b0 1 <b> (lo\u1ea1i) <\/b> <br\/> S\u1ed1 92388 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 2 + 3 + 8 + 8 = 30 <br\/> V\u00ec 30 = 3 . 9 + 3 n\u00ean 30 chia 9 d\u01b0 3 hay 92388 chia 9 d\u01b0 3 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> S\u1ed1 93148 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 3 + 1 + 4 + 8 = 25 <br\/> V\u00ec 25 = 9 . 2 + 7 n\u00ean 25 chia 9 d\u01b0 7 hay 93148 chia 9 d\u01b0 7 <b> (lo\u1ea1i) <\/b> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 chia 5 d\u01b0 3 v\u00e0 chia 9 d\u01b0 3 l\u00e0: 92388 <\/span> ","column":2}]}],"id_ques":552},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/7.jpg' \/><\/center> <br\/> Kh\u00f4ng th\u1ef1c hi\u1ec7n ph\u00e9p chia h\u00e3y t\u00ecm d\u01b0 khi chia $(10^{15} + 1)$ chia 3? <br\/>$(10^{15} + 1)$ : 3 d\u01b0 l\u00e0: _input_ ","hint":"N\u1ebfu s\u1ed1 A c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 chia 3 d\u01b0 m th\u00ec s\u1ed1 A chia 3 d\u01b0 m","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh t\u1ed5ng $(10^{15} + 1)$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> X\u00e9t t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a t\u1ed5ng v\u1eeba t\u00ednh \u1edf b\u01b0\u1edbc 1<br\/> N\u1ebfu t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a t\u1ed5ng tr\u00ean chia 3 d\u01b0 m th\u00ec t\u1ed5ng chia 3 d\u01b0 m <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $10^{15} + 1 = \\underbrace{100...0}_{15 \\text{ch\u1eef s\u1ed1 0}} + 1 = \\underbrace{100...01}_{14 \\text{ch\u1eef s\u1ed1 0}}$ <br\/> S\u1ed1 $\\underbrace{100..01}_{14 \\text{ch\u1eef s\u1ed1 0}}$ c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 2 n\u00ean $\\underbrace{100...01}_{14 \\text{ch\u1eef s\u1ed1 0}}$ chia 3 d\u01b0 2 <br\/> V\u1eady $(10^{15} + 1)$ chia 3 d\u01b0 2 <br\/> <span class='basic_pink'> S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2 <\/span> <br\/> "}]}],"id_ques":553},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["200"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/9.jpg' \/><\/center> <br\/> C\u00f3 bao nhi\u00eau s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 chia h\u1ebft cho 3 v\u00e0 kh\u00f4ng chia h\u1ebft cho 9 <br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_ ","hint":"S\u1ed1 c\u00e1c s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1 chia h\u1ebft cho 3 m\u00e0 kh\u00f4ng chia h\u1ebft cho 9 = s\u1ed1 c\u00e1c s\u1ed1 chia h\u1ebft cho 3 - s\u1ed1 c\u00e1c s\u1ed1 chia h\u1ebft cho 9","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1:<\/b> T\u00ednh s\u1ed1 c\u00e1c s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 chia h\u1ebft cho 3 <br\/> T\u00ednh s\u1ed1 c\u00e1c s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 chia h\u1ebft cho 9 <br\/> <b> B\u01b0\u1edbc 2: <\/b> S\u1ed1 c\u00e1c s\u1ed1 chia h\u1ebft cho 3 v\u00e0 kh\u00f4ng chia h\u1ebft cho 9 = s\u1ed1 c\u00e1c s\u1ed1 chia h\u1ebft cho 3 - s\u1ed1 c\u00e1c s\u1ed1 chia h\u1ebft cho 9 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> X\u00e9t d\u00e3y c\u00e1c s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 chia h\u1ebft cho 3: 102; 105;108; ...; 999 <br\/> S\u1ed1 s\u1ed1 h\u1ea1ng c\u1ee7a d\u00e3y tr\u00ean l\u00e0: (999 - 102) : 3 + 1 = 300 (s\u1ed1) <br\/> X\u00e9t d\u00e3y c\u00e1c s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 chia h\u1ebft cho 9: 108; 117; 126; ...; 999 <br\/> S\u1ed1 s\u1ed1 h\u1ea1ng c\u1ee7a d\u00e3y tr\u00ean l\u00e0: (999 - 108) : 9 + 1 = 100 (s\u1ed1) <br\/> S\u1ed1 c\u00e1c s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1 chia h\u1ebft cho 3 v\u00e0 kh\u00f4ng chia h\u1ebft cho 9 l\u00e0: <br\/> 300 - 100 = 200 (s\u1ed1)<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 200 <\/span> <br\/> "}]}],"id_ques":554},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["1"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/9.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 a, b sao cho a - b = 6 v\u00e0 $\\overline{7a5b1}$ chia h\u1ebft cho 3 <br\/> V\u1eady a = _input_; b = _input_ ","hint":"T\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a s\u1ed1 $\\overline{7a5b1}$ v\u00e0 d\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n c\u1ee7a b\u00e0i \u0111\u1ec3 t\u00ecm a, b ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1:<\/b> T\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a s\u1ed1 $\\overline{7a5b1}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> D\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n a - b = 6 \u0111\u1ec3 t\u00ecm a, b <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a s\u1ed1 $\\overline{7a5b1}$ l\u00e0: 7 + a + 5 + b + 1 = 13 + a + b (1) <br\/> V\u00ec a, b l\u00e0 c\u00e1c ch\u1eef s\u1ed1 trong s\u1ed1 $\\overline{7a5b1}$ n\u00ean a; b = 0, 1, 2,..., 9 <br\/> V\u00ec a - b = 6 n\u00ean a $\\geq$ 6 <br\/> N\u1ebfu b = 0 $\\Rightarrow$ a = 6 $\\Rightarrow$ 76501 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 6 + 5 + 0 + 1 = 19<br\/> V\u00ec 19 $\\not \\vdots$ 3 $\\Rightarrow$ 76501 $\\not \\vdots$ 3 <b> (lo\u1ea1i) <\/b> <br\/> N\u1ebfu b = 1 $\\Rightarrow$ a = 7 $\\Rightarrow$ 77511 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 7 + 5 + 1 + 1 = 21 <br\/> V\u00ec 21 $\\vdots$ 3 $\\Rightarrow$ 77511 $\\vdots$ 3 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> N\u1ebfu b = 2, a = 8 $\\Rightarrow$ 78521 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 8 + 5 + 2 + 1 = 23 <br\/> V\u00ec 23 $\\vdots$ 3 $\\Rightarrow$ 78521 $\\not \\vdots$ 3 <b> (lo\u1ea1i) <\/b> <br\/> N\u1ebfu b = 3, a = 9 $\\Rightarrow$ 79531 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 9 + 5 + 3 + 1 = 25 <br\/> V\u00ec 25 $\\not \\vdots$ 3 $\\Rightarrow$ 79531 $\\not \\vdots$ 3 <b> (lo\u1ea1i) <\/b><br\/> V\u1eady v\u1edbi a = 7, b = 1 th\u00ec $\\overline{7a5b1}$ chia h\u1ebft cho 3 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n l\u1ea7n l\u01b0\u1ee3t \u0111i\u1ec1n l\u00e0: 7; 1 <\/span> <br\/> "}]}],"id_ques":555},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["8"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/9.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 a, b sao cho b - a = 6 v\u00e0 $\\overline{56a3b}$ chia h\u1ebft cho 2 v\u00e0 3 <br\/> V\u1eady a = _input_; b = _input_ ","hint":"D\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n b - a = 6 \u0111\u1ec3 t\u00ecm c\u00e1c c\u1eb7p s\u1ed1 a, b th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u1ee7a b\u00e0i ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1:<\/b> D\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n b - a = 6 \u0111\u1ec3 t\u00ecm c\u00e1c c\u1eb7p s\u1ed1 a, b <br\/> <b> B\u01b0\u1edbc 2: <\/b> Thay c\u00e1c gi\u00e1 tr\u1ecb a, b v\u00e0o s\u1ed1 $\\overline{56a3b}$ \u0111\u1ec3 t\u00ecm s\u1ed1 chia h\u1ebft cho 2 v\u00e0 3 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec a, b l\u00e0 c\u00e1c ch\u1eef s\u1ed1 trong s\u1ed1 $\\overline{56a3b}$ n\u00ean a; b = 0, 1, 2,..., 9 <br\/> V\u00ec b - a = 6 n\u00ean b $\\geq$ 6 <br\/> S\u1ed1 $\\overline{56a3b}$ chia h\u1ebft cho 2 n\u00ean b ch\u1ec9 nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb ch\u1eb5n <br\/> N\u1ebfu a = 0 $\\Rightarrow$ b = 6 $\\Rightarrow$ 56036 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0 5 + 6 + 0 + 3 + 6 = 20 <br\/> V\u00ec 20 $\\not \\vdots$ 3 $\\Rightarrow$ 56036 $\\not \\vdots$ 3 <b> (lo\u1ea1i) <\/b> <br\/> N\u1ebfu a = 1 $\\Rightarrow$ b = 7 <b> (lo\u1ea1i) <\/b> (v\u00ec b l\u1ebb) <br\/> N\u1ebfu a = 2, b = 8 $\\Rightarrow$ 56238 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 5 + 6 + 2 + 3 + 8 = 24 <br\/> V\u00ec 24 $\\vdots$ 3 $\\Rightarrow$ 56238 $\\vdots$ 3 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> N\u1ebfu a = 3, b = 9 <b> (lo\u1ea1i) <\/b> (v\u00ec b l\u1ebb) <br\/> V\u1eady v\u1edbi a = 2, b = 8 th\u00ec $\\overline{56a3b}$ chia h\u1ebft cho 2 v\u00e0 3 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n l\u1ea7n l\u01b0\u1ee3t \u0111i\u1ec1n l\u00e0: 2; 8 <\/span> <br\/> "}]}],"id_ques":556},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/10.jpg' \/><\/center> <br\/> Thay a b\u1eb1ng ch\u1eef s\u1ed1 th\u00edch h\u1ee3p \u0111\u1ec3 $\\overline{a2013a}$ chia h\u1ebft cho 88 <br\/> V\u1eady a = _input_ ","hint":"88 = 11 . 8 n\u00ean \u0111\u1ec3 $\\overline{a2013a}$ $\\vdots$ 88 th\u00ec $\\overline{a2013a}$ chia h\u1ebft cho 11 v\u00e0 8","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> D\u1ef1a v\u00e0o d\u1ea5u hi\u1ec7u chia h\u1ebft cho 8 v\u00e0 d\u1ea5u hi\u1ec7u chia h\u1ebft cho 11 \u0111\u1ec3 t\u00ecm a <br\/> D\u1ea5u hi\u1ec7u chia h\u1ebft cho 11: C\u00e1c s\u1ed1 c\u00f3 hi\u1ec7u c\u1ee7a t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng l\u1ebb v\u00e0 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng ch\u1eb5n chia h\u1ebft cho 11 th\u00ec chia h\u1ebft cho 11 <br\/> D\u1ea5u hi\u1ec7u chia h\u1ebft cho 8: S\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng t\u1ea1o th\u00e0nh s\u1ed1 chia h\u1ebft cho 8 th\u00ec s\u1ed1 \u0111\u00f3 chia h\u1ebft cho 8<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec 88 = 11 . 8 n\u00ean \u0111\u1ec3 $\\overline{a2013a}$ $\\vdots$ 11 th\u00ec $\\overline{a2013a}$ chia h\u1ebft cho 8 v\u00e0 chia h\u1ebft cho 11 <br\/> X\u00e9t 3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng $\\overline{13a}$, th\u1eed l\u1ea7n l\u01b0\u1ee3t c\u00e1c gi\u00e1 tr\u1ecb a = 1, 2, 3,...,9 <br\/> Ta th\u1ea5y v\u1edbi a = 6 th\u00ec 136 $\\vdots$ 8 <br\/> N\u00ean 620136 $\\vdots$ 8 <br\/> S\u1ed1 620136 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0 h\u00e0ng l\u1ebb l\u00e0: 6 + 0 + 3 = 9 <br\/> S\u1ed1 620136 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng ch\u1eb5n l\u00e0: 2 + 1 + 6 = 9 <br\/> Hi\u1ec7u c\u1ee7a t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng l\u1ebb v\u00e0 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng ch\u1eb5n l\u00e0: 9 - 9 = 0 <br\/> V\u00ec 0 $\\vdots$ 11 $\\Rightarrow$ 620136 $\\vdots$ 11 <br\/> V\u1eady v\u1edbi a = 6 th\u00ec $\\overline{a2013a}$ chia h\u1ebft cho 88 <br\/> <span class='basic_pink'> S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 6 <\/span> <br\/> <span class='basic_green'> <i> L\u01b0u \u00fd: Khi t\u00ecm \u0111i\u1ec1u ki\u1ec7n ho\u1eb7c t\u00ecm s\u1ed1 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u00f9ng chia h\u1ebft cho nhi\u1ec1u s\u1ed1, ch\u1eb3ng h\u1ea1n s\u1ed1 \u0111\u00f3 chia h\u1ebft cho 2, 3, 4, 5, 8, 9, 11,... th\u00ec ta t\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 s\u1ed1 \u0111\u00f3 chia h\u1ebft cho 2 v\u00e0 5 tr\u01b0\u1edbc (s\u1ed1 c\u00f3 t\u1eadn c\u00f9ng b\u1eb1ng 0), ti\u1ebfp theo l\u00e0 chia h\u1ebft cho 4; 25 (x\u00e9t hai ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng), chia h\u1ebft cho 8; 125 (x\u00e9t 3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng), chia h\u1ebft cho 11 (x\u00e9t hi\u1ec7u c\u1ee7a t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng ch\u1eb5n v\u1edbi t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 h\u00e0ng l\u1ebb); r\u1ed3i sau c\u00f9ng l\u00e0 chia h\u1ebft cho 3, 9 (t\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 trong s\u1ed1 \u0111\u00e3 cho) <\/b> <\/span> "}]}],"id_ques":557},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[["4"]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/11.jpg' \/><\/center> <br\/> Cho $M_{1}$ l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 chia 9 d\u01b0 3 <br\/> $M_{2}$ l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 chia 9 d\u01b0 4 <br\/> $M_{3}$ l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 chia 9 d\u01b0 7","select":["A. $91684 \\in M_{1}$","B. $85349 \\in M_{2}$","C. $75381 \\in M_{3}$","D. $9475 \\in M_{3}$"],"hint":"S\u1ed1 A c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 chia 9 d\u01b0 m th\u00ec A chia 9 d\u01b0 m","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> T\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a t\u1eebng s\u1ed1 trong \u0111\u00e1p \u00e1n <br\/> N\u1ebfu s\u1ed1 \u0111\u00f3 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 chia 9 d\u01b0 m th\u00ec s\u1ed1 \u0111\u00f3 chia 9 d\u01b0 m <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> +) S\u1ed1 91684 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 1 + 6 + 8 + 4 = 28 <br\/> V\u00ec 28 = 3 . 9 + 1 n\u00ean 28 chia 9 d\u01b0 1 hay 91684 chia 9 d\u01b0 1 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh ''$91684 \\in M_{1}$'' l\u00e0 <b> SAI <\/b> <br\/> +) S\u1ed1 85349 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 8 + 5 + 3 + 4 + 9 = 29 <br\/> V\u00ec 27 = 3 . 9 + 2 n\u00ean 29 chia 9 d\u01b0 2 hay 85349 chia 9 d\u01b0 2 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh ''$85349 \\in M_{2}$'' l\u00e0 <b> SAI <\/b> <br\/> +) S\u1ed1 75381 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 7 + 5 + 3 + 8 + 1 = 24 <br\/> V\u00ec 24 = 2 . 9 + 6 n\u00ean 24 chia 9 d\u01b0 6 hay 75381 chia 9 d\u01b0 6 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh ''$75381 \\in M_{3}$'' l\u00e0 <b> SAI <\/b> <br\/> +) S\u1ed1 9475 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 l\u00e0: 9 + 4 + 7 + 5 = 25 <br\/> V\u00ec 25 = 2 . 9 + 7 n\u00ean 25 chia 9 d\u01b0 7 hay 9475 chia 9 d\u01b0 7 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh ''$9475 \\in M_{3}$'' l\u00e0 <b> \u0110\u00daNG <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":558},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["153"]]],"list":[{"point":10,"width":80,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/8.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean nh\u1ecf nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 bi\u1ebft s\u1ed1 \u0111\u00f3 chia 4 d\u01b0 1, chia 25 d\u01b0 3.<br\/> V\u1eady s\u1ed1 c\u1ea7n t\u00ecm: _input_ ","hint":"D\u1ef1a v\u00e0o d\u1ea5u hi\u1ec7u chia h\u1ebft cho 4 v\u00e0 d\u1ea5u hi\u1ec7u chia h\u1ebft cho 25","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> S\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng t\u1ea1o th\u00e0nh s\u1ed1 chia h\u1ebft cho 4 (ho\u1eb7c 25) th\u00ec s\u1ed1 \u0111\u00f3 chia h\u1ebft cho 4 (ho\u1eb7c 25) <br\/> V\u00e0 ch\u1ec9 nh\u1eefng s\u1ed1 \u0111\u00f3 m\u1edbi chia h\u1ebft cho 4 (ho\u1eb7c 25) <\/span> <br\/><br\/> <span class='basic_green'> B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 c\u00f3 3 ch\u1eef s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $\\overline{abc}$ <br\/> X\u00e9t hai ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng $\\overline{bc}$ <br\/> V\u00ec nh\u1eefng s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng t\u1ea1o th\u00e0nh s\u1ed1 chia h\u1ebft cho 25 th\u00ec chia h\u1ebft cho 25 <br\/> N\u00ean \u0111\u1ec3 $\\overline{abc}$ $\\vdots$ 25 th\u00ec $\\overline{bc}$ b\u1eb1ng 00; 25; 50 ho\u1eb7c 75 <br\/> $\\Rightarrow$ \u0111\u1ec3 $\\overline{abc}$ chia 25 d\u01b0 3 th\u00ec $\\overline{bc}$ b\u1eb1ng 03; 28; 53 ho\u1eb7c 78 <br\/> Ta c\u00f3: 03 chia 4 d\u01b0 3 <b> (lo\u1ea1i) <\/b>, 28 $\\vdots$ 4 <b> (lo\u1ea1i) <\/b>, 53 chia 4 d\u01b0 1 <b> (th\u1ecfa m\u00e3n) <\/b>, 78 chia 4 d\u01b0 2 <b> (lo\u1ea1i) <\/b> <br\/> V\u00ec $\\overline{abc}$ l\u00e0 s\u1ed1 nh\u1ecf nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 n\u00ean a = 1 <br\/> V\u1eady a = 1, $\\overline{bc}$ = 53, s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 153 <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 153 <\/span> "}]}],"id_ques":559},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[["4"]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai11/lv3/img\/8.jpg' \/><\/center> <br\/> Cho $A = 5 + 5^2 + 5^3 + 5^4 + ... + 5^8 (a, b \\in \\mathbb{N})$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?","select":["A. $A \\not \\vdots$ 2 ","B. $A \\vdots 2$ ","C. $A \\vdots 5$","D. C\u1ea3 B v\u00e0 C \u0111\u1ec1u \u0111\u00fang"],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t chia h\u1ebft c\u1ee7a m\u1ed9t t\u1ed5ng","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t chia h\u1ebft c\u1ee7a m\u1ed9t t\u1ed5ng v\u00e0 c\u00e1c d\u1ea5u hi\u1ec7u chia h\u1ebft cho 2; 5 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3 v\u00ec 5 $\\vdots$ 5; $5^2$ $\\vdots$ 5, ...., $5^8$ $\\vdots$ 5 <br\/> $\\Rightarrow$ $(5 + 5^2 + 5^3 + ... + 5^8)$ $\\vdots$ 5 <br\/> Trong t\u1ed5ng A c\u00e1c s\u1ed1 h\u1ea1ng 5, $5^2$, $5^3$,...., $5^8$ \u0111\u1ec1u c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 5 <br\/> A c\u00f3 8 s\u1ed1 h\u1ea1ng n\u00ean ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 5 . 8 = 40 (hay A c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 0) <br\/> $\\Rightarrow$ A $\\vdots$ 2 <br\/> V\u1eady A chia h\u1ebft cho 2 v\u00e0 5 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":560}],"lesson":{"save":0,"level":3}}