Factorials are somewhat annoying

Number Theory Level 2

What is the biggest prime factor of 98 ! × 100 ! × 102 ! 97 ! × 99 ! × 101 ! \dfrac{98!\times 100! \times 102!}{97! \times 99! \times 101!} ?


The answer is 17.

Interliser 727 by Interliser 727 , 22, Malaysia

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1 solution

Chris H
Aug 4, 2018

The initial expression can be simplified to 98・100・102. The distinct prime factors of 98 are 2 and 7--for 100 there are 2 and 5--for 102, we have 2, 3, and 17. 17 is the biggest.

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