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Answer:

10^1-7   =3 ( Contains  zero 9 and ends with 3)

10^2-7  = 93(contains one 9 and ends with 3)

10^3-7 = 993( contains two 9s in consecutive positions and ends with 3)

10^4-7 = 9993 (contains three 9s in consecutive positions and ends with 3)

Similarly it can be seen that 

10^25- 7 =999999………..9993(will contain Twenty four 9s in succession and end with 3)  

 It can be seen that all the above numbers are divisible by 3.

Therefore 10^25-7 = 999999………..9993 is divisible by 3 and the quotient 333333………..3331 will be the other factor.

 

Answer

Ans. The number is divisible by 3.

Explanation: As the pattern goes, 10^1 - 7 = 3, 10^2 - 7 = 93, 10^3 - 7 = 993 ...
All these numbers are divisible by 3 since the sums of their digits of the respective numbers are divisible 3.
So, 10^25 - 7 is also divisible by 3.

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