Test you divisibility basics
Algebra
Level
pending
A six digit number is of the form xyzxyz where x,y,z are constants(eg.-123123). A number in this form will always be divisible by-
101
1001
29
111
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1 solution
xyzxyz=100000x+10000y+1000z+100x+(10y)+z =100000x+100x+10000y+(10)y+1000z+z =100x(1000+1)+10y(1000+1)+z(1000+1) =1001(100x)+1001(10y)+z(1001) =1001(100x+10y+z) therefore, the number will always be divisible by 1001.