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In the prime factorization of 12! + 15! + 18! + 21! + 24!, what is the exponent of 3?

 Nov 15, 2022
 #1
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Break it down and find the multiples of 3 in each factorial

In 12! it's 3^4

In 15! it's 3^5

In 18 it's 3^7

In 21 it's 3^8

In 24 it's 3^9

So, in all, the exponent should be 33

(Someone should double check this)

 Nov 15, 2022
 #2
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Factor  [12! + 15! + 18! + 21! + 24!]==620499499079093007897600 =

 

2^10×3^5×5^2×7×11×53×129169×189221423 (22 prime factors, 8 distinct)

 

The exponent of 3 = 5  or  3^5

 Nov 15, 2022

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