Convert into factorial ` 7,8,9,10,11, 12, 13, 14, 15.

Answer

To convert the numbers 7, 8, 9, 10, 11, 12, 13, 14, and 15 into factorial form, we can express each number as a product of factorials. Here’s how we can do it step by step:

### Step-by-Step Solution:

1. **Understanding Factorials**: Recall that the factorial of a number \( n \) (denoted as \( n! \)) is the product of all positive integers up to \( n \). For example, \( 5! = 5 \times 4 \times 3 \times 2 \times 1 \).

2. **Expressing Each Number**: We can express each number from 7 to 15 in terms of factorials:
- \( 7 = \frac{7!}{6!} \)
- \( 8 = \frac{8!}{7!} \)
- \( 9 = \frac{9!}{8!} \)
- \( 10 = \frac{10!}{9!} \)
- \( 11 = \frac{11!}{10!} \)
- \( 12 = \frac{12!}{11!} \)
- \( 13 = \frac{13!}{12!} \)
- \( 14 = \frac{14!}{13!} \)
- \( 15 = \frac{15!}{14!} \)

3. **Combining the Factorials**: Now, we can combine these expressions:
- The product of all these numbers can be written as:
\[ 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 13 \times 14 \times 15 = \frac{7!}{6!} \times \frac{8!}{7!} \times \frac{9!}{8!} \times \frac{10!}{9!} \times \frac{11!}{10!} \times \frac{12!}{11!} \times \frac{13!}{12!} \times \frac{14!}{13!} \times \frac{15!}{14!} \]

4. **Simplifying the Expression**: Notice that all terms cancel out except for \( 15! \) in the numerator and \( 6! \) in the denominator:
\[ = \frac{15!}{6!} \]

5. **Final Result**: Thus, the expression for the product of numbers from 7 to 15 in factorial form is:
\[ 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 13 \times 14 \times 15 = \frac{15!}{6!} \]

### Final Answer:
\[ 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 13 \times 14 \times 15 = \frac{15!}{6!} \]