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1.
\(ƯCLN\left(a,b\right)=7\)
\(\Rightarrow a,b\)chia hết cho 7
\(\Rightarrow a,b\in B\left(7\right)\)
\(B\left(7\right)=\left(0;7;14;21;28;35;42;49;56;63;70;77;84;91;98;105...\right)\)
a, vì a+b=56 \(\Rightarrow\)\(a\le56;b\le56\)
\(\Rightarrow a=56;b=0.a=0;b=56\)
\(a=7;b=49.a=49;b=7\)
\(a=14;b=42.a=42;b=14\)
\(a=21;b=35.a=35;b=21\)
\(a=b=28\)
b, a.b=490 \(\Rightarrow a< 490;b< 490\)
\(\Rightarrow\) \(a=7;b=70-a=70;b=7\)
\(a=14;b=35-a=35;b=14\)
c, BCNN (a,b) = 735
\(\Rightarrow a,b\inƯ\left(735\right)\)
\(Ư\left(735\right)=\left(1;3;5;7;15;21;35;49;105;147;245;735\right)\)
\(\Rightarrow\)\(a=7;b=105-a=105;b=7\)
2.
a+b=27\(\Rightarrow\)\(a\le27;b\le27\)
ƯCLN(a,b)=3
\(\Rightarrow a,b\in B\left(_{ }3\right)\in\left(0;3;6;9;12;15;18;21;24;27;30;...\right)\)
BCNN(a,b)=60
\(\Rightarrow a,b\inƯ\left(60\right)\in\left(1;2;3;4;5;6;10;12;15;20;60\right)\)
\(\Rightarrow\)\(a=12;b=15-a=15;b=12\)
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a, 10 . 27 - 27 : 9
= 270 - 3
= 263
b, 72 . 33 + 72 . 67
= 72 ( 33 + 67 )
= 72 . 100
= 49 . 100
= 4900
c, 490 - [ ( 128 + 22 ) : 3 . 22 ] - 7
= 490 - ( 150 : 3 . 4 ) - 7
= 490 - ( 50 . 4 ) - 7
= 490 - 200 - 7
= 290 - 7
= 283
Không tính giá trị hãy xét xem tổng nào chia hết cho 7:
a) 28 + 47+217
b)45 + 56 + 140
c) 37 + 40 + 490
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Tổng c vì 37+40=77chia hết cho 7 và 490 chia hết cho 7
=> 37+40+490 chia hết cho 7
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a, 125+70+375+230
= (125+375)+(70+230)
= 500+300 = 800
b, 7 2 . 33 + 7 2 . 67
= 49.33+49.67 = 49.(33+67) = 49.100 = 4900
c, 35.11+65.18+35.13+65.6
= 35.(11+13)+65.(18+6) = 35.24+65.24 = 24.(35+65) = 24.100 = 2400
d, 490 – {[(128+22):3. 2 2 ] – 7}
= 490 – {[150:3.4] – 7}
= 490 – {[50.4] – 7}
= 490 – {200 – 7}
= 490 – 193 = 297
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a,D=1+2+4+8+16+32+64+128+256+512+1024
D=(1+2)+4+8+16+32+64+128+256+512+1024
D=(4+4)+8+16+32+64+128+256+512+1024
D=(8+8)+16+32+64+128+256+512+1024
D=(16+16)+32+64+128+256+512+1024
D=(32+32)+64+128+256+512+1024
D=(64+64)+128+256+512+1024
D=(128+128)+256+512+1024
D=(256+256)+512+1024
D=(512+512)+1024
D=1024+1024
D=2048
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Vì ƯCLN(a; b) . BCNN(a; b) = 1 . b
=> ƯCLN(a; b) = 490 : 70 = 7
=> a = 7m; b = 7n; (m ; n) = 1
Tích của a . b = 490
=> 7m . 7n = 490
=> 49. mn = 490
=> mn = 490 : 49
=> mn = 10
Ta có bảng giá trị
m | 1 | 2 | ||||
n | 10 | 5 | ||||
a | 7 | 14 | ||||
b | 70 | 35 |
Vậy cặp số cần tìm là (7; 70) ; (14; 35)