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The image you provided contains a mathematical exercise focused on the decomposition of numbers into prime factors. Let's break down the problem:

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### Activity 2: Decomposition into Prime Factors

#### a) Decompose the number 40 as a product of prime numbers.

**The question asks:**  
- What product verifies the decomposition of 40?

**The possible decompositions shown:**
1. \( 4 \times 10 = 40 \)  
   (But 4 and 10 are not prime numbers, so this is not valid for prime factorization.)

2. \( 2 \times 2 \times 10 = 40 \)  
   (Further, 10 is not a prime number, so we can continue breaking it down.)

3. \( 2 \times 2 \times 2 \times 5 = 40 \)  
   (This is correct, as 2 and 5 are prime numbers.)

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#### b) Decompose the number 180 as a product of prime numbers.

To find the prime factorization of 180:

1. Start by dividing 180 by 2 (the smallest prime number):  
   \( 180 \div 2 = 90 \)

2. Divide 90 by 2:  
   \( 90 \div 2 = 45 \)

3. Now, 45 is not divisible by 2, so move to the next prime number, which is 3:  
   \( 45 \div 3 = 15 \)

4. Divide 15 by 3:  
   \( 15 \div 3 = 5 \)

5. Finally, 5 is already a prime number.

**So, the prime factorization of 180 is:**  
\[ 180 = 2 \times 2 \times 3 \times 3 \times 5 \]

Or, in exponential form:  
\[ 180 = 2^2 \times 3^2 \times 5 \]

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Would you like further details or have any questions? 

Here are some related questions to help deepen your understanding:

1. What is a prime factorization and why is it useful in mathematics?
2. How can you determine if a number is prime?
3. Can all numbers be broken down into prime factors? Why or why not?
4. How does prime factorization help in finding the greatest common divisor (GCD)?
5. What is the significance of expressing a number using exponents in prime factorization?

**Tip:** When performing prime factorizations, always start dividing by the smallest prime number and work your way up!

Decompose the numbers 40 and 180 into products of prime factors.

This exercise focuses on decomposing the numbers 40 and 180 into their prime factors. Learn how to break down 40 into 2 × 2 × 2 × 5 and 180 into 2^2 × 3^2 × 5, using fundamental prime factorization techniques. Suitable for students in Grades 5-7.

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