Breaking Down the Calculation: How 3628800 ÷ (24 × 120 × 1) Equals 1260

If you’ve come across the mathematical expression:

\[
\frac{3628800}{24 \cdot 120 \cdot 1} = 1260
\]

Understanding the Context

you’re not just looking at numbers — you’re decoding a clean, logical breakdown that reveals how division simplifies complex expressions. In this article, we’ll explore step-by-step how this division works and why the result is 1260.

Understanding the Components

Let’s examine the components in the denominator first:

If \( \frac{1}{2 \cdot 3^{10}}+\frac{2}{2^{2} \cdot 3^{9}}+\frac{3}{2 ...

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If \( \frac{1}{2 \cdot 3^{10}}+\frac{2}{2^{2} \cdot 3^{9}}+\frac{3}{2 ...
Решите пример: \(\frac{1}{1} \cdot \frac{4}{5} \cdot \frac{5}{6}\)
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Key Insights

\[
24 \cdot 120 \cdot 1
\]

Multiplying these values gives:

\[
24 \ imes 120 = 2880
\]

So the full expression becomes:

\[
\frac{3628800}{2880}
\]

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Final Thoughts

Simplifying the Division

Now evaluate:

\[
3628800 \div 2880
\]

To simplify this, look for common factors or perform direct division.

Breaking it down:

  • 3628800 is a well-known factorial: \(9! = 9 \ imes 8 \ imes 7 \ imes 6 \ imes 5 \ imes 4 \ imes 3 \ imes 2 \ imes 1 = 362880\), but wait — actually, \(10! = 3628800\), so \(3628800 = 10!\).
    - \(2880 = 24 \ imes 120\), as we calculated:
    \(24 = 8 \ imes 3\),
    \(120 = 8 \ imes 15 = 8 \ imes (5 \ imes 3)\),
    so \(2880 = 2^5 \ imes 3^2 \ imes 5 = 2^5 \cdot 3^2 \cdot 5\)

But rather than factorization, performing direct division clarifies the result:

\[
3628800 \div 2880 = ?
\]

We can rewrite the division as: