factorial divisibility clarification needed

[bmwhype]

What is N in each statement?
1. (n+2)! is divisible by 36
2. (n+2)! is divisible by 49

in factorial divisibility questions, do we look for the highest factors or the highest prime factors?

in #1, do we look for the lowest number of where we can derive 5 instances of 2?
36 = 6*6
or
36 = 2^5

in #2, do we look for numbers with one instance of 7, or two?
(N+2)! = 7
or
(N+2)! = 49

[krovvidy]

#1 (n+2)! must be greater than or equal to 6! i.e., n >= 4

#2 (n+2)! must be greater than or equal to 14! i.e., n >= 12

Agree?

[Kim2549]

I agree with krovvidy.


1. If (n+2)! is divisible by 36, then: (n+2)! should be divisible by 6^2, which is equivalent to (2x3)^2. So, (n+2)! should have the prime factors 2,2,3 and 3, and the least value of n, such that (n+2)! has all these factors is 6, and n>=4.

the same goes for #2.