Fun Factorial Problem

I hope you guys like it! Math is so fun!

[theunholybanana]

I used the less rigorous "5 is the only prime number counted twice so it's gotta be 10" method

[rockdavis]

Wow did not know that method I just checked it and wow it works!!! Thank o trust you now lol 😂😂😂!!!

[pjanderson]

This is the only case we know of where x!y!=z! And x or y isn’t equal to 1, 0 or z-1. Obviously any natural number x satisfies x!1!=x! and x!0!=x!, and then x!(x!-1)!=(x!)! For example 3!5!=6! Because 3!=6 or 4!23!=24! Because 4!=24. Other than these cases, 6!7!=10! Is the only other solution of x!y!=z! that we’ve been able to find.

[keinplaninmathe]

And I already wanted to try euler's gamma function...

Well played.

[timraster]

Great method. Not to be picky, but the answer should be: "X = 10"

[HaizamSanchez-eesx]

Wow, always learning something new, which i havent done in school yet. Its actually interesting how easy you can make math. Well done, keep going😊

[colinjava]

For a second I thought I needed the gamma function 😂

[sufiyanas]

I would have done by factorisation but this one is even better

[yusufsheikh]

Bro, you can just cheese it by using prime factors. There are 2 5s and no 11, therefore x is at least 10, but since theres no 11 its less than that. So x is 10

[mikejonesTML]

I've never taken an advanced math class.
So this question I'm about to ask is, not me being facetious.
What are the real world applications of the factorial system?

[lol-rlwq]

Dose multiplying factorials always result in a factorial

[aminelahlou]

Funny thing: 10! Is exactly the amount of seconds in 6 weeks!

[mrscsi]

edit: apparently i did it the long way lol

well 7! is just 6! * 7, so the answer is 6!*6!*7
i know 6! is 720
we can make this simpler by splitting off the zeros

720*720=72*72*100

now we foil the 72

(70*70)+(70*2)+(70*2)+(2*2)
4900+140+140+4=
4900+284=
5184

now we put it back into the previous expression

6!*6!=720*720=5184*100=518400

518400*7=

now we can split off the zeros again but i’ll skip that for you


=
10000*7 = 70000
8000*7=56000
400*7=2800


+ 70000
+ 56000
+ 2800=
3628800

if you know your factorials this number should look familiar

it’s 10! so x=10

[cragasm]

not sure if the exclamation mark should be used as factorial, when people wanna yell numbers some people mistake it with factorial

[Gattrecity]

I think of making a formula for when you are multiplying 2 factorials it gives you the factorial that their product make

[thatsamoore]

It’s been too long since I’ve done math. I immediately said 42 😂

[redroach]

Is thre a wat to solve algebraic? I have been trying using the gamma function, but I can't seem to get anywhere

[kenbutsuri]

You can also use gamma functions and plot it :D

[kenbutsuri]

Are there any other cases where there are solutions for whole numbers?

[davidseed]

easy way.
6!=720 =8×9×10.
and 7! x 8×9×10 =10!
so x=10