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

Guest Nov 8, 2022

#2**+2 **

ok so we break it down

12! has 4 "3" factors and 1 "9" factor

so that's 1+4=5

15! has 5 "3's" and 1 "9"

so that's 5+1=6

18! has 6 "3's" and 2 "9's"

so that's 6+2=8

21! has 7 "3's" and 2 "9's"

so that's 7+2=9

24! has 8 "3's" and 2 "9's"

so that's 8+2=10 factors of 3

so its basicaly 3^5 + 3^6 + 3^8 + 3^9 + 3^10

simplify that to (3^5)(1 + 3 + 3^3 + 3^4 + 3^5)

1 + 3 + 3^3 + 3^4 + 3^5 is not divisible by 3

so it's 3^5

I think

yaytomath Nov 9, 2022