The number of odd factors of 90 is ………… .

Answer

To find the number of odd factors of the number 90, we can follow these steps:

### Step 1: Prime Factorization of 90
First, we need to find the prime factorization of 90.

90 can be factored as:
- 90 = 2 × 45
- 45 = 3 × 15
- 15 = 3 × 5

So, the prime factorization of 90 is:
\[ 90 = 2^1 \times 3^2 \times 5^1 \]

### Step 2: Identify Odd Factors
Odd factors are those factors that do not include the prime factor 2. Therefore, we will only consider the odd prime factors, which are 3 and 5.

From the prime factorization, we can see:
- The exponent of 3 is 2 (which means we can have 0, 1, or 2 of the factor 3).
- The exponent of 5 is 1 (which means we can have 0 or 1 of the factor 5).

### Step 3: Calculate the Number of Odd Factors
To find the total number of odd factors, we use the formula:
\[ (\text{exponent of 3} + 1) \times (\text{exponent of 5} + 1) \]
Substituting the values we found:
- For 3: exponent is 2, so we have \(2 + 1 = 3\)
- For 5: exponent is 1, so we have \(1 + 1 = 2\)

Now, calculating the total number of odd factors:
\[ 3 \times 2 = 6 \]

### Conclusion
The number of odd factors of 90 is **6**.

---