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2015-03-26T21:31:48+05:30

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2²°°⁸ + 10²⁰⁰⁸=2²°°⁸+2²°°⁸.5²°°⁸=  2²°°⁸(1+ 5²°°⁸)  so the largest power of 2 that divides 2²°°⁸ + 10²⁰⁰⁸ is 2008                                   
2 5 2
2015-03-27T09:09:18+05:30
Here is your answer
2²°°⁸ + 10²⁰⁰⁸
=2²°°⁸+2²°°⁸.5²°°⁸
=  2²°°⁸(1+ 5²°°⁸)  
so the largest power of 2 that divides 2²°°⁸ + 10²⁰⁰⁸
is 2008  
1 5 1