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