`{:("Quantity A","Quantity B"),("The number of distinct prime","The number of distinct prime"),("factors of 40","factors of 50"):}`

Answer

To solve the problem of comparing the number of distinct prime factors of 40 and 50, we will follow these steps:

### Step 1: Find the prime factorization of 40
To find the distinct prime factors of 40, we start by determining its prime factorization.

1. Divide 40 by the smallest prime number, which is 2:
\[ 40 \div 2 = 20 \]
2. Divide 20 by 2 again:
\[ 20 \div 2 = 10 \]
3. Divide 10 by 2 once more:
\[ 10 \div 2 = 5 \]
4. Finally, 5 is a prime number.

Thus, the prime factorization of 40 is:
\[ 40 = 2^3 \times 5^1 \]
The distinct prime factors of 40 are 2 and 5.

### Step 2: Count the distinct prime factors of 40
From the prime factorization, we see that the distinct prime factors of 40 are:
- 2
- 5

Therefore, the number of distinct prime factors of 40 (Quantity A) is:
\[ \text{Quantity A} = 2 \]

### Step 3: Find the prime factorization of 50
Next, we will find the distinct prime factors of 50.

1. Divide 50 by the smallest prime number, which is 2:
\[ 50 \div 2 = 25 \]
2. Next, divide 25 by the next smallest prime number, which is 5:
\[ 25 \div 5 = 5 \]
3. Finally, divide 5 by 5:
\[ 5 \div 5 = 1 \]

Thus, the prime factorization of 50 is:
\[ 50 = 2^1 \times 5^2 \]
The distinct prime factors of 50 are 2 and 5.

### Step 4: Count the distinct prime factors of 50
From the prime factorization, we see that the distinct prime factors of 50 are:
- 2
- 5

Therefore, the number of distinct prime factors of 50 (Quantity B) is:
\[ \text{Quantity B} = 2 \]

### Step 5: Compare Quantity A and Quantity B
Now we compare the two quantities:
\[ \text{Quantity A} = 2 \quad \text{and} \quad \text{Quantity B} = 2 \]

Since both quantities are equal, we conclude that:
\[ \text{Quantity A} = \text{Quantity B} \]

### Final Answer
Both quantities are equal.

---