1. All odd numbers less than 9 are irranged in a descending order a) Write down the number formet in i) Figures ii) Wonds b) What is the total value of the third digit in the number? Express each of the following as a product of its prime factors a) 594 b) 960 c) 30375 d) 2025

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### **1. Arranging Odd Numbers Less Than 9 in Descending Order**

**a) Writing the Number in Different Formats**

- **List of Odd Numbers Less Than 9:**  
  The odd numbers less than 9 are: **1, 3, 5, 7**

- **Descending Order:**  
  Arranged in descending order: **7, 5, 3, 1**

- **i) In Figures:**  
    The number formed is **7531**

- **ii) In Words:**  
    **Seven thousand five hundred thirty-one**

**b) Total Value of the Third Digit in the Number**

- **Number:** 7531

- **Identifying the Third Digit:**  
  The digits from left to right are:
  
  1. **7** (Thousands place)
  2. **5** (Hundreds place)
  3. **3** (Tens place)
  4. **1** (Units place)
  
  The **third digit** is **3**, which is in the **tens place**.

- **Total Value of the Third Digit:**  
  $$ 3 \times 10 = 30 $$

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### **2. Prime Factorization of Given Numbers**

**a) 594**

- **Step-by-Step Factorization:**
  $$
  594 = 2 \times 297 \
  297 = 3 \times 99 \
  99 = 3 \times 33 \
  33 = 3 \times 11 \
  $$
  
- **Prime Factors:**  
  $$ 594 = 2 \times 3^3 \times 11 $$

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**b) 960**

- **Step-by-Step Factorization:**
  $$
  960 \div 2 = 480 \
  480 \div 2 = 240 \
  240 \div 2 = 120 \
  120 \div 2 = 60 \
  60 \div 2 = 30 \
  30 \div 2 = 15 \
  15 = 3 \times 5 \
  $$
  
- **Prime Factors:**  
  $$ 960 = 2^6 \times 3 \times 5 $$

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**c) 30,375**

- **Step-by-Step Factorization:**
  $$
  30375 \div 5 = 6075 \
  6075 \div 5 = 1215 \
  1215 \div 5 = 243 \
  243 = 3^5 \
  $$
  
- **Prime Factors:**  
  $$ 30,375 = 3^5 \times 5^3 $$

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**d) 2,025**

- **Step-by-Step Factorization:**
  $$
  2025 \div 5 = 405 \
  405 \div 5 = 81 \
  81 = 3^4 \
  $$
  
- **Prime Factors:**  
  $$ 2,025 = 3^4 \times 5^2 $$

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### **Summary of Prime Factorizations**

- **594:** $$ 2 \times 3^3 \times 11 $$
- **960:** $$ 2^6 \times 3 \times 5 $$
- **30,375:** $$ 3^5 \times 5^3 $$
- **2,025:** $$ 3^4 \times 5^2 $$

If you have any further questions or need additional explanations, feel free to ask!
**1. Arranging Odd Numbers Less Than 9 in Descending Order** - **a) Number Formats:** - **Figures:** 7531 - **Words:** Seven thousand five hundred thirty-one - **b) Total Value of the Third Digit:** - The third digit is 3, which is in the tens place. Its total value is 30. **2. Prime Factorizations** - **594:** $$ 2 \times 3^3 \times 11 $$ - **960:** $$ 2^6 \times 3 \times 5 $$ - **30,375:** $$ 3^5 \times 5^3 $$ - **2,025:** $$ 3^4 \times 5^2 $$

1. All odd numbers less than 9 are irranged in a descending order a) Write down the number formet in i) Figures ii) Wonds b) What is the total value of the third digit in the number? Express each of the following as a product of its prime factors a) 594 b) 960 c) 30375 d) 2025

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