To find the highest power of 48 in 32!, we need to determine the highest power of 48 that can be obtained by dividing 32! without any remainder.

Let's break down the problem into smaller steps:

Step 1: Prime factorization of 48
To find the highest power of 48, we need to analyze its prime factorization. Prime factorization of 48 can be done as follows:

48 = 2 * 2 * 2 * 2 * 3 = (2^4) * 3

Step 2: Prime factorization of 32!
Next, we need to find the prime factorization of 32!. To do this, we need to find all the prime numbers less than or equal to 32 and determine their powers in the factorial.

Prime numbers less than or equal to 32 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

Now, let's determine the powers of these prime numbers in 32!:

Power of 2 in 32! = floor(32/2) + floor(32/4) + floor(32/8) + floor(32/16) = 16 + 8 + 4 + 2 = 30
Power of 3 in 32! = floor(32/3) + floor(32/9) = 10 + 3 = 13
Power of 5 in 32! = floor(32/5) = 6
Power of 7 in 32! = floor(32/7) = 4
Power of 11 in 32! = floor(32/11) = 2
Power of 13 in 32! = floor(32/13) = 2
Power of 17 in 32! = floor(32/17) = 1
Power of 19 in 32! = floor(32/19) = 1
Power of 23 in 32! = floor(32/23) = 1
Power of 29 in 32! = floor(32/29) = 1
Power of 31 in 32! = floor(32/31) = 1

Step 3: Determine the highest power of 48
To find the highest power of 48, we need to find the highest power of 2 and 3 that can be obtained from the prime factorization of 48 and the prime factorization of 32!.

The highest power of 2 = min(power of 2 in 48, power of 2 in 32!) = min(4, 30) = 4
The highest power of 3 = min(power of 3 in 48, power of 3 in 32!) = min(1, 13) = 1

Therefore, the highest power of 48 in 32! is 4.

Answer: A. 4