There are four prime numbers written in ascending order. The product of the first three is 1001 and that of the last three is 2431. The last number is :

Options

A. 17
B. 19
C. 23
D. 13

Answer

To solve the problem, we need to find four prime numbers in ascending order such that the product of the first three is 1001 and the product of the last three is 2431. Let's denote the four prime numbers as A, B, C, and D, where A < B < C < D.

### Step-by-Step Solution:

1. **Identify the product of the first three primes**:
We know that:
\[ A \times B \times C = 1001 \]

2. **Factor 1001 into prime numbers**:
To find the prime factors of 1001, we can perform prime factorization:
\[ 1001 = 7 \times 11 \times 13 \]
Thus, we can assign:
\[ A = 7, \quad B = 11, \quad C = 13 \]

3. **Identify the product of the last three primes**:
We also know that:
\[ B \times C \times D = 2431 \]

4. **Substitute the values of B and C**:
We substitute B and C into the equation:
\[ 11 \times 13 \times D = 2431 \]

5. **Calculate the product of B and C**:
First, we calculate:
\[ 11 \times 13 = 143 \]

6. **Solve for D**:
Now we can solve for D:
\[ D = \frac{2431}{143} \]
Performing the division:
\[ D = 17 \]

7. **Conclusion**:
The four prime numbers in ascending order are:
\[ 7, 11, 13, 17 \]
Therefore, the last prime number D is:
\[ \boxed{17} \]