The largest power of 2 that divides  2 ²⁰⁰⁸  +  10²⁰⁰⁸ is ?????/ RATES PROMISED

2009

2 ²⁰⁰⁸ + 10 ²⁰⁰⁸

= 2 ²⁰⁰⁸    x  ( 1 + 5²⁰⁰⁸  )

Also

1 + 5²⁰⁰⁸  ends with 6

so, 1 + 5²⁰⁰⁸  is also divisible by 2

let 1 + 5²⁰⁰⁸  = 2p

so,

2 ²⁰⁰⁸    x  ( 1 + 5²⁰⁰⁸  )   =   2 ²⁰⁰⁸   x  (2p)

                                            =  2 ²⁰⁰⁹ p

Hence the ans. is 2009

(10)^2008 =(2*5)^2008.

so, split it ...  (2^2008) *(5^2008)

inside it will form (1+ 5^2008).

and this 1 will combine with odd no. 5^2008 to generate one more power of 2.

so, it's 2009 that's max possible ower of 2.

 The solution given by Pradeep Rout is good... He took 1+ 5²⁰⁰⁸ as 2p. But when ew take 2 outside we will either 3 or 8 in the unit's place. If t is 3 answer is correct... If its 8 the maximum power is nt 2009.