Googol this.

Number Theory Level 4

It is a well known fact that 1 1 followed by 100 100 zeroes is a number called g o o g o l googol . Now, you have to find out the value of the sum of the number of digits in g o o g o l 2 googol^{2} and the distinct prime factors it has.


The answer is 208.

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Krishna Ar by Krishna Ar , 21, India

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2 solutions

Nicolas Bryenton
Sep 19, 2014

Googol=10^100

Googol^2=10^200 => 201 digits (1 fol.owed by 200 zeroes)

It's a power of ten: 2 and 5 are the only prime factors

201+5+2=208

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Sakshi Taparia
Feb 11, 2015

googol is 1 followed by 100 zeroes. So, googol^2 will be 1 followed by 200 zeroes. therefore, no of digits = 201

further, 1 followed by 200 zeroes = 10^2 = (2*5)^2

hence, distinct prime factors are 2 and 5.

therefore, final ans. = 201 +2 +5 =208

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