Let's solve the expression:

\[
\frac{10! + 11! + 12!}{144}
\]

### Step 1: Calculate the factorials.
- \( 10! = 10 \times 9 \times 8 \times \dots \times 1 = 3,628,800 \)
- \( 11! = 11 \times 10! = 11 \times 3,628,800 = 39,916,800 \)
- \( 12! = 12 \times 11! = 12 \times 39,916,800 = 479,001,600 \)

### Step 2: Sum the factorials.
\[
10! + 11! + 12! = 3,628,800 + 39,916,800 + 479,001,600 = 522,547,200
\]

### Step 3: Divide by 144.
\[
\frac{522,547,200}{144} = 3,627,400
\]

Thus, the value of the expression is:
\[
\boxed{3,627,400}
\]

Would you like more details on any of these steps or further explanation?

### Related questions:
1. How do you simplify complex factorial expressions?
2. Can you explain properties of factorial growth?
3. What are some practical applications of factorials in real life?
4. How can division be simplified when handling large numbers?
5. What other operations can you perform on factorials?

### Tip: Factorials grow very quickly, so breaking them down in steps helps avoid mistakes.

Learn how to solve the factorial expression (10! + 11! + 12!) / 144 with a step-by-step breakdown. This problem covers factorials, summation, and division. Suitable for high school students in Grades 9-12.

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