Question

8.Determinați numerele divizibile cu 9, de forma:
a)15a; b)2a9; c)333a; d)12ab0.

Answer 1

un nr e divizibil cu 9 daca suma cifrelor sale e divizibila cu 9 (e multiplu de 9)
a) 15a
1+5+a=6+a={9} => a=3
15a=153

b)2a9
2+a+9=11+a=M 9=> 11+a=18; a=7
2a9=279

c) 333a
3+3+3+a=9+a M9 => a+9={9, 18}; a={0,9}
333a={3330,3339}

d) 12ab0
1+2+a+b+0=3+a+b=M9=> 3+a+b={9,18}; a+b={6,15}
pt a+b=6=> (a,b)={(0,6),(1,5),(2,4),(3,3),(4,2),(5,1),(6,0)}
12ab0={12060,12150,12240,12330,12420,12510,12600}
pt a+b=15=>(a,b)={(6,9),(7,8),(8,7),(9,6)}
12ab0={12690,12780,12870,12960}

12ab0={12060,12150,12240,12330,12420,12510,12600,12690,12780,12870,12960}