Can you factorise this?

Number Theory Level 3

Find the the largest prime factor of the number 99899.


The answer is 353.

Puneet Pinku by Puneet Pinku , 20, India

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2 solutions

Puneet Pinku
Mar 25, 2016

Clearly the largest prime factor is 353.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ratul Pan
Mar 25, 2016

By hit and trial we find that,
31 8 2 − 3 5 2 = 99899 318^{2}-35^{2} = 99899
Therefore,
99899 = ( 353 ) ( 283 ) 99899=(353)(283)
Since 353 and 283 are prime numbers hence,
353 \boxed{353} is the largest prime factor of 99899



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