Find the prime factorization of 1352 using the ladder method.

To find the prime factorization of 1352 using the ladder method, we'll divide the number by the smallest prime factors step by step until we reach 1. Here's how it works:

### Step-by-Step Ladder Method:

1. **Divide by 2 (the smallest prime number):**

   \[
   1352 \div 2 = 676
   \]

2. **Divide by 2 again:**

   \[
   676 \div 2 = 338
   \]

3. **Divide by 2 once more:**

   \[
   338 \div 2 = 169
   \]

4. **169 is not divisible by 2, so try the next prime number, 13:**

   \[
   169 = 13 \times 13
   \]

So, the prime factorization of 1352 is:

\[
1352 = 2 \times 2 \times 2 \times 13 \times 13
\]

or, more compactly:

\[
1352 = 2^3 \times 13^2
\]

### Summary:
- Prime factorization of 1352 using the ladder method is \(2^3 \times 13^2\).

Would you like further details, or have any questions? Here are some related topics you might find interesting:

1. How to use the ladder method for other numbers.
2. Why prime factorization is useful in mathematics.
3. Differences between ladder and factor tree methods.
4. How to identify prime numbers quickly.
5. Applications of prime factorization in real-life problems.

**Tip:** Always start with the smallest prime when using the ladder method; it makes the process smoother and more efficient!

Discover how to find the prime factorization of 1352 step-by-step using the ladder method. This guide covers essential number theory concepts and demonstrates how to break down numbers into their prime factors. Ideal for students in Grades 6-8.

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