1. **State the problem:** Find the prime factors of 27. 2. **Recall the definition:** Prime factors are the prime numbers that multiply together to give the original number. 3. **Start factorization:** 27 is a positive integer. We check the smallest prime number 2, but 27 is not divisible by 2. 4. **Try next prime 3:** 27 divided by 3 equals 9, so 3 is a prime factor. 5. **Continue factoring 9:** 9 divided by 3 equals 3, so another 3 is a prime factor. 6. **Factor 3:** 3 divided by 3 equals 1, so the last prime factor is 3. 7. **Write the prime factorization:** $$27 = 3 \times 3 \times 3 = 3^3$$ **Final answer:** The prime factors of 27 are 3, 3, and 3, or simply $$3^3$$.