Can you solve this tricky factorial problem?

What do you think about this question? If you're reading this ❤️. Have a great day!

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[Paddy-ipqk]

¿Por qué la gran mayoría de gente que viene aquí a comentar piensa que TODOS los videos de matemática en YouTube están dirigidos únicamente a grandes eruditos que ya conocen todos los métodos y que son capaces de resolverlos mentalmente? Existen personas que recién se inician en la matemática a quienes les resulta útil una explicación paso a paso y con mucho detalle. Si ese no es tu caso, cierra el video y vete a ver otro, pero no dejes tu mala vibra aquí ni critiques que no lo haya resuelto en 20 segundos. Si en verdad tienen gusto por la matemática, sepan que las tonterías que dicen no ayudan en nada a que esta bella ciencia se siga difundiendo.

[stevenmayhew]

Here's another one: 5!x3!=6! because 3!=6 and 5!x6=6!. So, that's two cases: 6!x7!=10! and 3!x5!=6!. Put them together and you get that 3!x5!x7!=10!.

[tamirerez]

DID YOU KNOW?
The number of seconds in 6 weeks is 10!

[hippophile]

Here's my solution method:
Assuming there is an answer, x must have two factors of 5, as both 6! and 7! have obviously both only one factor of 5, so for the 5-factors to balance, you need two in x!. Thus it must be at LEAST 10!
However, it cannot have a factor of 11 (as 7! has not got far enough for that). So the only possible asnwe is x=10. Then it is a simple matter of checking.

[myfyrmadocjones]

9:25 Not the only case where a factorial is a multiple of two factorials - you also have 6! = 3! X 5!

[simmmr.]

There's no need to factorise the 7! as a product:
→ x=10

[AlephThree]

X! will include 7! as it is greater than 7!. So you know 6!=8*9*…*”x”. 6! Is 720 which is 8*9*10 so x=10.

[prashnaprashant]

Nice warm up as well as easy question.

[vaclavkrpec]

This wasn't tricky, I didn't even need to write it down. Take 2 x 4 from the 6!, that gives you 8! on the right hand side. You're left with 3 x 5 x 6. That's 90 = 9 x 10. That gives you 10! on the right hand side, equal to x!, ergo x = 10.

[Gnowop]

Seeing so many of the same problem floating around in FB, YouTube, I can even remember the answer immediately as 10!

[prashnaprashant]

Can you make videos on IIT JEE ADVANCE OR MAINS question?

[archangecamilien]

Not that tricky, actually, lol...x! (x being an integer, no gamma function stuff, lol) will be a factorial, only certain numbers can be "factorials", like 1, 2, 6, 24, 120, 720, if I'm not mistaken...try to see which of these is equal to 7*8*...*n for some n, etc...as soon as you "hit" one that is equal to such a product, etc, bingo!, lol...Just try each of them, 7*8, then 7*8*9 until you hit a "factorial" number...

[KingGisInDaHouse]

Multiply the 6! To the other side and you recursively divide until you get one to reverse the factorial.

[astrolad]

11 is the smallest prime > 7. So the answer must be 8!., 9!, or 10!. And 6! must be equal to 8, or 8*9 (72), or 8*9*10 (720). 6! is 720, so the answer is 10!.

[jollyjoker]

6! = 2*3*4*5*6 needs to divide into numbers starting from 8; Remove 2 and 4 leaving 3*5*6, 9; remove 3 and half the 6, leaving 5*2=10. Edit: First time one of these videos has the same solution I came up with!

[nichtvonbedeutung]

You can also multiply 7*8*9*10 at the end and then divide the result by 1*2*3*4*5*6*7 and the result should be 1.

[krwada]

It is not that difficult. 7! = 7 x 6! ... You just need to do a prime factorization of 6! and work your way up. Prime Factorization of (6!) = 2x3x5x2x2x3x2

Start working way up
x8 = cross out three (2)
x9 = cross out two (3)
x10 = cross out two (2) and five (5)

You will see that at this point all factors of 6! are crossed out. That is 8x9x10 = 6!

Therefore, x = 10

[arikahn]

Note that answer must be less than 11 since 11 is prime and not a factor in 7!

[markmajkowski]

IF there’s an answer it must be at least 7 to get a 7 in the product and at least 10 to get a 5 and not be more than 10 or it has an 11. Nothing wrong with Guess and Check.

[xyz]

A little silly to expand 7! It has to grow from 7!, first thing is to find a 8 from the expansion of 6!