The prime factorization of **300** can be found by dividing the number by the smallest prime number and continuing this process until only prime numbers are left.

1. Start by dividing 300 by the smallest prime number, 2:
   \[
   300 \div 2 = 150
   \]
2. Divide 150 by 2 again:
   \[
   150 \div 2 = 75
   \]
3. Now divide 75 by the next smallest prime number, 3:
   \[
   75 \div 3 = 25
   \]
4. Divide 25 by the next smallest prime number, 5:
   \[
   25 \div 5 = 5
   \]
5. Finally, divide 5 by 5:
   \[
   5 \div 5 = 1
   \]

Thus, the prime factorization of **300** is:
\[
300 = 2^2 \times 3 \times 5^2
\]

Would you like more details on any part of the process?

Here are 5 related questions:
1. What is the prime factorization of 600?
2. How can you determine if a number is prime?
3. What are the common factors between 300 and 500?
4. How can prime factorization help with finding the greatest common divisor (GCD)?
5. How do you find the least common multiple (LCM) using prime factorization?

**Tip:** Prime factorization is useful for simplifying fractions and finding LCM or GCD of numbers.

Discover the prime factorization of 300 with a clear, step-by-step guide. This explanation covers essential number theory concepts like dividing by prime numbers, using the fundamental theorem of arithmetic, and simplifying 300 to 2^2 × 3 × 5^2. Ideal for students in Grades 5-7.

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