1. **State the problem:** Find the exponent of 3 in the prime factorization of 2025. 2. **Recall the prime factorization process:** To find the exponent of a prime in a number, repeatedly divide the number by that prime until it is no longer divisible. 3. **Start dividing 2025 by 3:** $$2025 \div 3 = 675$$ 4. **Divide 675 by 3:** $$675 \div 3 = 225$$ 5. **Divide 225 by 3:** $$225 \div 3 = 75$$ 6. **Divide 75 by 3:** $$75 \div 3 = 25$$ 7. **Check if 25 is divisible by 3:** It is not, so stop here. 8. **Count the number of times 3 divides 2025:** It divides 4 times. 9. **Therefore, the exponent of 3 in the prime factorization of 2025 is:** $$\boxed{4}$$