last 6 digit

The positive powers of five have a compact, repeating pattern in their ending m digits, in the powers of five from 5^m on. For example: starting with 5, their last digit is always 5; starting with 25, their last two digits are always 25; starting with 125, their last three digits alternate between 125 and 625. These cycles come in lengths of powers of two.

therefore the last m digits will have a cyclicity of 2^m-2....
so last 6 digits of 5 will have a cylicity of 16 starting from 5¹⁶ which has 015625 in the last 6 digits...
to find the last 6 digits of 2010 x 5²⁰¹⁴ we need to find the last six digits of 5²⁰¹⁴....
and 2014 is of the form 6+16n only.....thus last six digits of 5²⁰¹⁴ will be 015625 and the last six digits of 2010 x 5²⁰¹⁴ will be 406250.....