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What is the largest n so that 5^n is a factor of 98! + 99! + 100!?

 Nov 2, 2019

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Factor  [98! + 99!  + 100!] =

 

2^99×3^46×5^26×7^16×11^8×13^7×17^5×19^5×23^4×29^3×31^3×37^2×41^2×43^2×47^2×53×59×61×67×71×73×79×83×89×97 (240 prime factors, 25 distinct)

 

As you can see, the largest 5^n =5^26

 Nov 2, 2019
 #1
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+1
Best Answer

Factor  [98! + 99!  + 100!] =

 

2^99×3^46×5^26×7^16×11^8×13^7×17^5×19^5×23^4×29^3×31^3×37^2×41^2×43^2×47^2×53×59×61×67×71×73×79×83×89×97 (240 prime factors, 25 distinct)

 

As you can see, the largest 5^n =5^26

Guest Nov 2, 2019

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