Question

Prime factorization of 20!

Answer 1

really?

Answer 2

2*2*5*19*1*2*3*3*17*1*2*2*2*2*3*5*7*2*13*2*3*2*11*5*2*3*3*2*2*2*7*3*2*5*2*2*3*2*1=20! lol!!!!!

Answer 3

some fancy method? all the primes from 2 to 20 will be there for sure
answer is
\[2^{18}×3^8×5^4×7^2×11×13×17×19\]

Answer 4

never tried this before but is lovely

Answer 5

someone plz check it wid my ans

Answer 6

ok i will rewrite what you wrote. easier to see without the ones
\[2*2*5*19*2*3*3*17*2*2*2*2*3*5*7*2*13*2*3*2*11\]
\[*5*2*3*3*2*2*2*7*3*2*5*2*2*3*2=20! \]

Answer 7

my god it matches how did u get it satellite

Answer 8

Just making sure u were all awake....:-)

Answer 9

grind it till you find it. you know all the primes from 2 to 19 will be there. then just a matter of how many times right? basically what you did. there may be some snap way to do it but not so clear from the pattern

Answer 10

U know 11 to 19 are there once, 7 twice (7 and 14), 5 in 5,10,15,20 etc..

Answer 11

got it had read it somewhere long ago
no of twos=[20/2]+[20/4]+[20/8]+[20/16]+[20/32]
where [] stand for greatest integer

Answer 12

or maybe you can do this. how many 5s?
5,10,15,20 4 of them
how many 7's?
7,17 2
a little harder for the 3's right?

Answer 13

because you can't just count. you have to count 9 and 18 twice

Answer 14

i meant 7, 14 2 of them doh

Answer 15

no of 3's=[20/3]+[20/9]+[20/27]=8
my method works!!

Answer 16

cool!

Answer 17

dont remember the derivatn though

Answer 18

ok cool but i am not sure i understand

Answer 19

look [ ] stands for greates integer like [20/3]=6 we ignre things after decimal

Answer 20

why
\[[\frac{20}{3}]+[\frac{20}{3^2}]+[\frac{20}{3^3}]\]

Answer 21

no i get what it means, but how do you know to use the denominators 3,3^2,3^3
how do you know when to stop?

Answer 22

oh never mind dumb question

Answer 23

since that is 0

Answer 24

as u go further [20/27] =0 so u keep adding 00

Answer 25

so u stop at 9

Answer 26

yeah <dopeslap>

Answer 27

hahaha

Answer 28

so lets try how many 3's in 30!

Answer 29

10+3+1=14

Answer 30

[30/3]+[30/9]+[30/27]=10+3+1

Answer 31

cool. now why?

Answer 32

Multiplicative functions

Answer 33

i think it is like this
20/3 gives how many mutiples of 3 before20 so as we keep adding 20/9 it 3 repeats in a no. divisible by 9 so we add it again and so on

Answer 34

god i love the internet. if they had this when i was in school i would have had several degrees by now!
http://2000clicks.com/mathhelp/NumberTh10FactorialDivisors.aspx

Answer 35

yeah you have the reasoning. thanks!

Answer 36

@estudier, did you know this question was so interesting when you posted?