Blow your head up 3!

Number Theory Level 3

Find the total number of factors of the integer 22467198509345. 22467198509345.


The answer is 8.

Yuxuan Seah by Yuxuan Seah , 20, Singapore

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1 solution

Yuxuan Seah
Jun 28, 2014

Note that 22467198509345 = 5 × 67 × 67066264207 22467198509345 = 5 \times 67 \times 67066264207 .

Hence, the number of factors of 22467198509345 22467198509345 is equivalent to : 2 × 2 × 2 = 8 2\times2\times2=\boxed{8}

Check: Let 67066264207 = x 67066264207=x

We find that the factors of 22467198509345 22467198509345 are 1 , 5 , 67 , x , 5 x , 67 x , 335 , 335 x , 1, 5, 67, x, 5x, 67x, 335, 335x, and we are done.

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Note that 22467198509345 = 5 × 67 × 67066264207 22467198509345 = 5 \times 67 \times 67066264207 .

LOL!

Daniel Liu - 6 years, 11 months ago

how do you decide 67066264207 is prime ?

Sunil Pradhan - 6 years, 10 months ago

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GOOGLING LOL

math man - 6 years, 9 months ago

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what lol I think in the examination time you will be in trouble you must tell the method @math man

sakshi rathore - 5 years, 11 months ago

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