Simplifying expressions: complete simplification does not simplify factorials if there are numbers present!

This could be a very trivial question, so I apologize from the beginning. I would like to do something that Mathematica could do less than a month ago. In particular, consider the following expression

$ frac { sqrt { frac {(m + 6)! (m + 6)} {(m + 5)!}}} {(m + 2)!} $

Simplify completely for this (assuming that m> = 0)

$ frac {6 + m} {Gamma[3+m]$

So far so good. However, if now I consider

$ frac { sqrt { frac {(m + 6)! (m + 6)} {(m + 5)!}}} {1024 (m + 2)!} $

Fullsimplify will give

$ frac {0.000976563 sqrt { frac {(m + 6.)! (m + 6.)} {(m + 5.)!}}} {(m + 2.)!} $.

My question is, what am I doing wrong? Why, simply by adding a number, FullSimplify he is no longer able to give me

$ frac {6 + m} {1024 Gamma[3+m]$ Without touching the numbers that appear?

Code:

Assuming[ m >= 0  , 
 Sqrt[(((6 + m) (6 + m)!)/(5 + m)!)] / (1024 (2 + m)!) // FullSimplify]

Simplification of expressions: Fullsimplify does not simplify the factorials if Numeber is present!

This could be a very trivial question, so I apologize from the beginning. I would like to do something that Mathematica could do less than a month ago. In particular, consider the following expression

$ frac { sqrt { frac {(m + 6)! (m + 6)} {(m + 5)!}}} {(m + 2)!} $

Simplify completely for this (assuming that m> = 0)

$ frac {6 + m} {Gamma[3+m]$

So far so good. However, if now I consider

$ frac { sqrt { frac {(m + 6)! (m + 6)} {(m + 5)!}}} {1024 (m + 2)!} $

Fullsimplify will give

$ frac {0.000976563 sqrt { frac {(m + 6.)! (m + 6.)} {(m + 5.)!}}} {(m + 2.)!} $.

My question is, what am I doing wrong? Why, just by adding a number, simplify completely I can not give myself anymore

$ frac {6 + m} {1024 Gamma[3+m]$ Without touching the numbers that appear?

Code:

Assuming[ m >= 0 ,
Sqrt[(((6 + m) (6 + m)!)/(5 + m)!)] / (1024 (2 + m)!) // FullSimplify]