Question

Determine the largest multiple of 6 which divides 14! Explain your work.

Answer 1

14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1

Rewrite the right side in the form of 6k where k is some number

Answer 2

make sure k is as large as possible

Answer 3

im having trouble understanding. are you saying 12 is the answer?

Answer 4

no, 12 isn't the answer

Answer 5

can you rearrange 14*13*12*11*10*9*8*7*6*5*4*3*2*1 into the form of 6k

Answer 6

how?

Answer 7

is there a 6 anywhere in that list?

Answer 8

yea

Answer 9

ok pull that out and rewrite into the form 6k where k is some number

Answer 10

ok i pull out 6k, then what?

Answer 11

im not getting this

Answer 12

14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1

14! = 6*14*13*12*11*10*9*8*7*5*4*3*2*1

14! = 6*(14*13*12*11*10*9*8*7*5*4*3*2*1)

Answer 13

and then i just calculate it?

Answer 14

yeah calculate everything after the 6*

Answer 15

is the answer within the parenthesis or is it the answer after i multiply that all by six

Answer 16

the result after you multiply all that out in the parenthesis

Answer 17

because that will give you the multiple of 6

Answer 18

that's a factor of 14!

Answer 19

yea but is the answer what's in the parenthesis? or that times 6

Answer 20

whatever is in the parenthesis, multiply that out

Answer 21

and that's the answer whatever k is

Answer 22

yes

Answer 23

thanks

Answer 24

np