Question

Cho abc + deg chia hết cho 37. Chứng minh rằng: abcdeg chia hết cho 37

Answer 1

Ta có : A = abcdeg - (abc+deg)

             = abc.1000 + deg - abc - deg

             = abc.999

             = abc.27.37

=> A chia hết cho 37

Vì abc + deg chia hết cho 37 mà A chia hết cho 37 nên abcdeg chia hết cho 37 

Answer 2

\(\overline{abc}+\overline{deg}⋮37\)

\(\overline{abcdeg}=1000\cdot\overline{abc}+deg\)

\(\Rightarrow999\cdot\overline{abc}+\overline{abc}+\overline{deg}\)

\(\Rightarrow\left(\overline{abc}\cdot27\cdot37\right)+\overline{abc}+\overline{deg}\)

Do \(\overline{abc\cdot37\cdot27⋮37}\)nên \(\overline{abcdeg}⋮37\)

Answer 3

 /abcdeg = 1000./abc + /deg 
/abcdeg = 999./abc + /abc + /def 
/abcdeg = 37.27./abc + /abc + /deg (*) 
(*) ta có: 
/abc + /deg chia hết cho 37 => VP chia hết cho 37 => VT = /abcdeg chia hết 37

Answer 4

37 chuan 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000%

Answer 5

Ta có:
A= abcdeg - ( abc+deg)
   = abc.1000 + deg - abc - beg
   = abc.999
   = abc.27.37
=> A chia hết cho 37
Vì :
          abc + deg chia hết cho 37 mà A chia hết cho 37 nên abcdeg chia hết cho 37