The prime factorization of 171 is 3 × 57. To break it down further, we can factor 57 as well. Since 57 can be divided by 3, we find that 57 = 3 × 19. Therefore, the complete prime factorization of 171 is:
171 = 3 × 3 × 19 or 3² × 19
To explain this process: we start with 171 and check for divisibility by the smallest prime number, which is 2. 171 is odd, so it’s not divisible by 2. Next, we try 3 by adding the digits (1 + 7 + 1 = 9), and since 9 is divisible by 3, so is 171. Dividing 171 by 3 gives us 57. We then repeat this with 57, again dividing by 3, which gives us 19, another prime number. Therefore, the prime factors of 171 are 3 and 19, with 3 appearing twice.