If 2004 is split after the third digit into a three-digit integer and a one-digit integer, then the two integers, 200 and 4, have a common factor greater than one. The years 2005 and 2006 each have this same property, too.

What is the first odd-numbered year after 2006 that has this property?

2013

Step-by-step explanation:

Given that the year 2004 if split after the third digit into a three-digit integer and a one-digit integer, then the two integers, 200 and 4,

200 and 4 have a common factor 4.

Similarly for year 2005, we have 200 and 5 have a common factor 5

and 2006, 200 and 6 have a common factor 2.

Next odd numbers would be

2007, 2009, 2011, 2015 and so on.

If we split we get 200, 7 or 200, 9, only which do not have this property

Next would be 201, 1 or 201, 3 ...

201 and 3 have common factor 3

So 2013 is the first odd numbered year after 2006 which has this property