Find the prime factorization of 2025 . \( \square \) Hint

To find the prime factorization of 2025, we can start by dividing it by the smallest prime numbers. 1. **Check divisibility by 3**: The sum of the digits of 2025 is \(2 + 0 + 2 + 5 = 9\), which is divisible by 3. So, we can divide 2025 by 3: \[ 2025 \div 3 = 675 \] 2. **Continue with 675**: Again, check if 675 is divisible by 3. The sum of the digits is \(6 + 7 + 5 = 18\), which is also divisible by 3: \[ 675 \div 3 = 225 \] 3. **Continue with 225**: Check if 225 is divisible by 3. The sum of the digits is \(2 + 2 + 5 = 9\), which is divisible by 3: \[ 225 \div 3 = 75 \] 4. **Continue with 75**: Check if 75 is divisible by 3. The sum of the digits is \(7 + 5 = 12\), which is divisible by 3: \[ 75 \div 3 = 25 \] 5. **Continue with 25**: Now, 25 is not divisible by 3, so we check the next prime number, which is 5. Since 25 ends in 5, it is divisible by 5: \[ 25 \div 5 = 5 \] 6. **Finally, divide 5 by itself**: \[ 5 \div 5 = 1 \] Now we can summarize the prime factorization: \[ 2025 = 3^4 \times 5^2 \] Thus, the prime factorization of 2025 is: \[ \boxed{3^4 \times 5^2} \]