Prime factorization related functions: prime factor to its power and power of prime [duplicate]

Question

FactorInteger can be used to perform prime factorization:

FactorInteger[5^2 7^3 11^4]

Results in:

{{5,2},{7,3},{11,4}}

Is there a function that given an integer will return the value of a given prime factor raised to its power?

E.g. let's say the function is F:

F[5^2 7^3 11^4, 5]    returns: 5^2
F[5^2 7^3 11^4, 7]    returns: 7^3
F[5^2 7^3 11^4, 11]   returns: 11^4

Also, is there a function that will return the power of a given prime?

E.g. let's say the function is G:

G[5^2 7^3 11^4, 5]    returns: 2
G[5^2 7^3 11^4, 7]    returns: 3
G[5^2 7^3 11^4, 11]   returns: 4

Answer 1

Your G is called IntegerExponent[] in Mathematica:

Table[IntegerExponent[5^2 7^3 11^4, k], {k, {5, 7, 11}}]
   {2, 3, 4}

You should now be able to use that function to write your function F.