To prime factorize 1000, we need to find the prime numbers that multiply together to give 1000.

1. Start with the smallest prime number, which is 2. Since 1000 is even, it is divisible by 2:
\[ 1000 \div 2 = 500 \]
\[ 1000 = 2 \times 500 \]

2. Continue dividing by 2:
\[ 500 \div 2 = 250 \]
\[ 1000 = 2^2 \times 250 \]

3. Divide by 2 again:
\[ 250 \div 2 = 125 \]
\[ 1000 = 2^3 \times 125 \]

4. Now, 125 is not divisible by 2, so move to the next prime number, which is 3. 125 is not divisible by 3 either. Move to the next prime number, which is 5:
\[ 125 \div 5 = 25 \]
\[ 1000 = 2^3 \times 5 \times 25 \]

5. Continue dividing by 5:
\[ 25 \div 5 = 5 \]
\[ 1000 = 2^3 \times 5^2 \times 5 \]

6. Finally, divide by 5 again:
\[ 5 \div 5 = 1 \]
\[ 1000 = 2^3 \times 5^3 \]

So, the prime factorization of 1000 is:
\[ 1000 = 2^3 \times 5^3 \]

Would you like more details or have any questions?

Here are some related questions:
1. What is prime factorization?
2. How do you find the prime factors of a number?
3. What are prime numbers?
4. Why is prime factorization important in mathematics?
5. Can you provide another example of prime factorization?
6. How does prime factorization help in finding the greatest common divisor (GCD)?
7. How does prime factorization help in finding the least common multiple (LCM)?
8. Are there any efficient algorithms for prime factorization?

**Tip:** Always start with the smallest prime number and work your way up when performing prime factorization.

Explore the step-by-step process of prime factorizing 1000 into its prime components. Learn how to apply divisibility rules and identify prime numbers. Suitable for students in Grades 5-8.

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