Find the prime factorisation of 825 , 675,450

Let's find the prime factorization of each number.

### 1. **Prime factorization of 825:**
- Start by dividing by 3 (smallest prime factor):  
  \( 825 \div 3 = 275 \)
- Now, divide 275 by 5 (next prime factor):  
  \( 275 \div 5 = 55 \)
- Divide 55 by 5:  
  \( 55 \div 5 = 11 \)
- 11 is a prime number.

So, the prime factorization of 825 is:  
\( 825 = 3 \times 5^2 \times 11 \)

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### 2. **Prime factorization of 675:**
- Start by dividing by 3:  
  \( 675 \div 3 = 225 \)
- Divide 225 by 3:  
  \( 225 \div 3 = 75 \)
- Divide 75 by 3:  
  \( 75 \div 3 = 25 \)
- Now, divide by 5:  
  \( 25 \div 5 = 5 \)
- Divide by 5 again:  
  \( 5 \div 5 = 1 \)

So, the prime factorization of 675 is:  
\( 675 = 3^3 \times 5^2 \)

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### 3. **Prime factorization of 450:**
- Start by dividing by 2 (smallest prime factor):  
  \( 450 \div 2 = 225 \)
- Divide by 3:  
  \( 225 \div 3 = 75 \)
- Divide by 3 again:  
  \( 75 \div 3 = 25 \)
- Now, divide by 5:  
  \( 25 \div 5 = 5 \)
- Divide by 5 again:  
  \( 5 \div 5 = 1 \)

So, the prime factorization of 450 is:  
\( 450 = 2 \times 3^2 \times 5^2 \)

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### Summary:
1. \( 825 = 3 \times 5^2 \times 11 \)
2. \( 675 = 3^3 \times 5^2 \)
3. \( 450 = 2 \times 3^2 \times 5^2 \)

Do you want further details or have any questions?  
Here are some related questions to explore:

1. What is the greatest common divisor (GCD) of 825, 675, and 450?
2. How do you find the least common multiple (LCM) of 825, 675, and 450?
3. Can you explain why prime factorization is important in solving GCD and LCM problems?
4. What are the prime factors of 900?
5. How does the fundamental theorem of arithmetic relate to prime factorization?

**Tip:** Always start with the smallest prime factor when finding the prime factorization, and divide progressively until you reach 1.

Find the prime factorisation of 825, 675, 450

Discover how to find the prime factorization of 825, 675, and 450 through a detailed breakdown using division. Learn important concepts in number theory and the application of the Fundamental Theorem of Arithmetic. This guide is perfect for students in Grades 6-8.

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