To find the prime factorization of the number 300, we can start by dividing it by the smallest prime number and continue factoring until we reach all prime numbers.
- Start with 300:
- Divide by 2 (the smallest prime number): \[ 300 \div 2 = 150 \]
- Next, divide 150 by 2: \[ 150 \div 2 = 75 \]
- Now, 75 is not divisible by 2 anymore, so we move to the next prime number, which is 3:
- Divide 75 by 3: \[ 75 \div 3 = 25 \]
- Next, divide 25 by the next prime number, which is 5:
- Divide 25 by 5: \[ 25 \div 5 = 5 \]
- Finally, divide 5 by 5: \[ 5 \div 5 = 1 \]
Now, we have completely factored 300. Combining all the divisors, we find:
- Two 2's (from the two divisions by 2)
- One 3 (from the division by 3)
- Two 5's (from the two divisions by 5)
Putting this together, the prime factorization of 300 is: \[ 300 = 2^2 \times 3^1 \times 5^2 \]
You've listed the prime factors as 2, 3, 5, and 5. The only prime factor missing from your list is 5 (this is the factor we need to count twice to account for both occurrences).
Thus, the missing prime factor is: \[ \text{5} \]
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