The number of 2 digit numbers having exactly 6 factors is :

Answer

To find the number of two-digit numbers that have exactly 6 factors, we need to understand how the number of factors of a number is determined based on its prime factorization.

### Step-by-Step Solution:

1. **Understanding the Factor Count Formula**:
The number of factors of a number \( n \) with the prime factorization \( n = p_1^{e_1} \times p_2^{e_2} \times ... \times p_k^{e_k} \) is given by:
\[ (e_1 + 1)(e_2 + 1)...(e_k + 1) \]
To have exactly 6 factors, we can have two cases:
- Case 1: \( n = p^5 \) (where \( p \) is a prime number)
- Case 2: \( n = p^2 \times q \) (where \( p \) and \( q \) are distinct prime numbers)

2. **Case 1: \( n = p^5 \)**:
- The smallest prime number is 2. Thus, we calculate \( 2^5 = 32 \).
- The next prime is 3, and \( 3^5 = 243 \) which is not a two-digit number.
- Therefore, the only two-digit number in this case is **32**.

3. **Case 2: \( n = p^2 \times q \)**:
- Here, we need to find combinations of \( p^2 \) and \( q \) such that the product is a two-digit number.
- The primes we consider for \( p \) are 2, 3, 5, and 7 (since \( 11^2 = 121 \) is not a two-digit number).
- We calculate \( p^2 \) for these primes:
- For \( p = 2 \): \( 2^2 = 4 \)
- For \( p = 3 \): \( 3^2 = 9 \)
- For \( p = 5 \): \( 5^2 = 25 \)
- For \( p = 7 \): \( 7^2 = 49 \)

Now we will pair each \( p^2 \) with distinct primes \( q \) to find valid two-digit products:
- \( 4 \times q \): \( q = 3, 5, 7, 11, 13 \) gives \( 12, 20, 28, 44, 52 \) (all valid)
- \( 9 \times q \): \( q = 2, 5, 7, 11 \) gives \( 18, 45, 63, 99 \) (all valid)
- \( 25 \times q \): \( q = 2, 3 \) gives \( 50, 75 \) (both valid)
- \( 49 \times q \): \( q = 2 \) gives \( 98 \) (valid)

4. **Listing All Valid Two-Digit Numbers**:
From the calculations:
- From \( 4 \): \( 12, 20, 28, 44, 52 \)
- From \( 9 \): \( 18, 45, 63, 99 \)
- From \( 25 \): \( 50, 75 \)
- From \( 49 \): \( 98 \)

Thus, the valid two-digit numbers with exactly 6 factors are:
\[ 12, 18, 20, 28, 44, 45, 50, 52, 63, 75, 98, 99 \]

5. **Counting the Numbers**:
We have the numbers: \( 12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 75, 98 \).
Counting these gives us a total of **16** two-digit numbers that have exactly 6 factors.

### Final Answer:
The number of two-digit numbers having exactly 6 factors is **16**.