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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?

 May 25, 2020
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Let's try the odd numbers after 2006:

 

2007   --->   200 and 7   -->   No, 200 is not divisible by 7.

2009   --->   200 and 9   -->   No, 200 is not divisible by either 3 or 9.

2011   --->   201 and 1   -->   No, 1 has no divisor greater than 1.

2013   --->   201 and 3   -->   Yes, both 201 and 3 are divisible by 3.

 May 25, 2020

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