All multiples of 10 have this property. n=10a becomes 100a which is 10n.
If n=10a+b with 0<b<10 and a>0, adding the zero creates
100a+b and we seek the ratio to be an integer:
(100a+b)/(10a+b)=m
solving for a gives
a=b(1m)/(10(m10))
Since m<10 this makes for an easy search. For each m, try to find a b that makes a a whole number.
There are three solutions:
m=6, b=8, a=1
m=7, b=5, a=1
m=9, b=5, a=4
corresponding to
18*6=108
15*7=105
45*9=405

Posted by Jer
on 20160321 12:30:42 